The Sm-Nd isotopic method in the geochronology laboratory of the University of Brasília

The Sm-Nd Isotopic Method in the Geochronology Laboratory of the University of Brasília

S.M.C.L. GIOIA and M.M. PIMENTEL^*

Universidade de Brasília, Instituto de Geociências,

Laboratório de Geocronologia, Cx. Postal 04465, 70910-900 Brasília, DF

Manuscript received November 3, 1998; accepted for publication on November 9, 1999;

contributed by M.M. PIMENTEL

ABSTRACT

Nd isotopes represent one of the best tools to investigate the processes involved in the evolution of the continental crust and mantle. This is due mainly to the similar geochemical behaviour of Sm and Nd, both light rare earth elements, which inhibits their fractionation during most varied geological processes. In order to carry out crustal evolution studies in central Brazil, the Sm-Nd isotopic method was implanted at the Geochronology Laboratory of the University of Brasília. The Sm-Nd separation methodology is basically that described in Richard et al. (1976), with the addition of some improvements. In this study we describe in detail the methodology used in Brasília. Precision and accuracy were checked with the international standards such as JB-3, BCR-1, BHVO-1 and La Jolla, and the following results were found: JB-3 (Nd=15.74 ppm and Sm=4.28 ppm), BCR-1 (¹⁴³Nd/¹⁴⁴Nd=0.512647±8, Nd=28.73 ppm and Sm=6.66 ppm), BHVO-1 (Nd=24.83 ppm and Sm=6.2 ppm) and La Jolla (¹⁴³Nd/¹⁴⁴Nd=0.511835±14).

Key words: Sm-Nd method, isotope dilution, ion exchange chromatography, TIMS.

INTRODUCTION

The Sm-Nd geochronometer is based on the decay of Sm to ¹⁴³Nd, with the emission of an particle. The equation below describes the Sm-Nd isotopic evolution for any geological system:

Equation (1) can also be written as:

The age t of the system can be calculated after the determination of ¹⁴³Nd/¹⁴⁴Nd and Sm/¹⁴⁴Nd ratios. Thermal Ionisation Mass Spectrometry (TIMS) is the most commonly used technique for the determination of isotopic ratios and also for the determination of REEs concentrations by isotope dilution. The isotopic analysis is the mass spectrometer is preceded by chemical treatment, involving the addition of a spike solution, dissolution of the sample and the chemical extraction of Sm and Nd by ion exchange. The extraction of Sm and Nd are accomplished in two stages. The first stage consists of the bulk separation of lanthanide fraction and in the second stage, the elements are separated from each other in order to avoid isobaric interference and also the presence of elements that make the ion beam unstable or that interfere with the ionisation efficiency of Sm and Nd.

This work reports an efficient method of micro-extraction used for Sm and Nd separation, based on the method employed by Richard et al. (1976).

METHODOLOGY

SUMMARY OF PREVIOUS CHEMICAL SEPARATION METHODS

Precise and accurate determination of isotopic ratios of metals cannot be achieved if they have not been efficiently separated from other interfering elements. If traces of elements of the matrix are present in the aliquot to be analyzed, isobaric interference can happen (Potts 1987). In the pioneer work of Ketelle & Boyd (1951), the difficulty to obtain efficient separation of each element of the REE group, was stressed.

The method most commonly applied in the separation of Sm and Nd for isotopic analyses of geological samples is described in Richard et al. (1976). It firstly uses an ion exchange column for the REE separation, followed by chromatography of reverse phase in order to separate Sm and Nd. This second column is packed with polytetrafluorethylene powder (PTFE), impregnated with DI-(2-etilexil) phosphoric acid (HDEHP).

This method, however, is not capable of separating Ce and Pr, which are present in substantial amounts in the Nd fraction (White & Patchett 1984). The presence of Ce, for instance, can make the ion beam unstable if present in large amounts (Whitehouse 1989). Whitehouse (1989) describes a method capable of reducing the amount of Ce in the Nd fraction, oxidating from Ce to Ce with KBrO and passing the solution through a HDEHP micro-column of approximately 1 cm. Another method that uses the classic ion exchange chromatography for the separation of the REEs was introduced by Eugster et al. (1970) and Dosso & Murthy (1980), where the fractions of Sm and Nd are separated in a secondary column packed with a cationic resin of the ion ammonium type. The elements are separated as organometalic complexes formed with the 2-hidroxi-isobutiric acid (-HIBA). The method presents good resolution, and the fractions of Sm and Nd are practically free from other interfering elements. It is, however, a tedious and time-consuming method and the results do not present significant differences from those obtained by the previous method. Less commonly used is the method that uses the anion exchange resin and acetic acid - nitric acid and methanol as eluent (Hooker et al. 1975, O'Nions et al. 1977). It is more efficient than the one that uses HDEHP, however it is necessary to work with the Nd isotope which has Ce, as an important isobaric interferent. A fast technique is the chromatography of high resolution Liquid Chromatography of High Resolution - HPLC (High Performance Liquid Chromatography), and Ionic Chromatography of High Resolution - HPIC (High Performance Ion Chromatography) which present high resolution and speed (Cassidy & Chauvel 1989).

SEPARATION TECHNIQUE USED IN BRASÍLIA

In Brasília we decided for the method using the HDEHP, with the use of the commercial LN-spec resin. This also consists of teflon powder impregnated with HDEHP, industrially prepared with a very small grain size (270 to 150 mesh). It presented very good efficiency for the separation of Ce and this element is almost totally absent in the Nd fractions (isobaric with Ce). Another form of eliminating the interference of Ce is to avoid the use of Nd isotope for fractionation and isotope dilution calculations.

Significant amounts of Pr were found in the Nd fraction, however this element does not represent an interferent when Nd isotopic measurements are done in the metallic form (Nd) instead of the oxide form, when small interference with Pr oxides, with masses 158 and 159 happen (Richard et al. 1976). In the same way, samples with high Ba concentrations, can also present an ineffective separation of Ba in the secondary column, which was proven to the case in the experiments in this study. However this does not interfere either in the Nd measurement, because it is ionized before the Nd analysis start due to its lower ionisation temperature (Thirwall 1982). Most of the Ba can be removed during the process of chromatographic separation, eluting the solution with HNO in a cationic resin, before the secondary elution for separation of Sm and Nd (Verma 1991), or still using the methodology presented by Stray & Dahlgren (1995), which combines classic chromatography of ionic change and HPIC for the separation and quantification of REEs in geological samples, based on the method of Le Roex & Watkins (1990).

The separation procedure used in the University of Brasília was efficient for the separation of Sm and Nd and, although time consuming, the procedure is simple and sufficiently effective. This is based, firstly, in the separation of the REE group, using a cation resin (primary column) followed by the extraction of Nd and Sm through a partition separation of phase-reverse (HDEHP), both using HCl as eluent.

EXTRACTION OF Sm AND Nd OF ROCK SAMPLES

Sample Digestion

50 to 100 mg of rock sample is mixed with the spike and the mixture is dissolved in teflon bombs covered with a steel jacket, using 1 mL of distilled conc. HNO and 4 mL of concentrated and distilled HF. Dissolution is followed by evaporation using a mounted evaporation system with infrared lamps and teflon capsules. The residue is taken again in HF:HNO (4:1) mixture and back to the oven at ca. 190C for 4 days. After complete dissolution, the sample was dried down and 2 mL of concentrated HNO were added. The solution was dried down again, a new attack with 6 mL of distilled 6N HCl follows. The solution should be absolutely clear and homogeneous at this stage. Complete evaporation of the solution sample and addition of 2 mL of distilled 2.5N HCl follows. During the course of the study the evaporation procedure was modified. Samples are now evaporated on hot plates, inside clean air cabinets (class-100 air) placed in fume cupboards. This allows cleaner environment for the evaporation, and also allows the evaporation of a large number of samples at the same time.

As already observed in other studies (Getty et al. 1993, Rehkamper et al. 1996 and Sato 1998), we had successful attacks using Savilex® capsules. Some samples, however, such as garnet-rich rocks and some ultramaphic rocks were not entirely dissolved and needed to be transferred to bombs.

Separation of the REEs (Calibration of the Primary Column)

A quartz column (i.d. = 8 mm and height = 15 cm) was packed with 2.2g (it evaporates for 60C) or 12 cm of cation resin Bio-Rad AG 50W-X8 200-400 mesh in aqueous solution. The sample solution is eluted in the column using HCl (Fig. 1). The REE group is collected in the fraction between 1 and 15 mL of 6N HCl, after elution with 32 mL of 2.5N HCl. Together, with the REEs, Y and Ba are also collected (Richard et al. 1976). The column is regenerated with ca. 15 mL of 6N HCl and stored in diluted acid solution.

Fig. 1
- Separation of the REE group from the main elements of the rock.

The 2.5N HCl was standardized by titrimetry, with NaCO (anhydrous) as base and methyl orange as indicator.

Separation of Sm and Nd (Calibration of the Secondary Column)

The secondary columns are made of teflon (Savilex®) (i.d. = 5 mm and height = 10 cm) and packed with LN-Spec resin (liquid resin HDEHP-270-150 mesh powdered teflon coated with di-ethylexil phosphoric acid). Height of resin bed is 6.5 cm. The REE fractions were totally evaporated and re-dissolved in 200 L of 0.18N HCl. This solution was loaded into the LN-Spec column. The Nd fraction was collected in 4 mL of 0.3N HCl after the initial 10 mL of 0.18N HCl (Fig. 2). After the extraction of Nd, 2 mL of 0.3N HCl were discarded and the Sm fraction was collected in 4 mL of 0.4N HCl, with a flow speed of 1 mL/30 min. The regeneration of the resin was achieved with 6 mL of 6N HCl. The column was conditioned again with the purified 3 mL of HO (Nanopure) followed by 23 mL of 0.18N HCl.

Fig. 2
- Sm and Nd separation. The calibration was made with LN-spec resin (HDEHP resin impregnated in teflon powder of 150-270 mesh). HCl was used as eluent in the calibration.

CHROMATOGRAPHIC COLUMNS FOR MINERALS

Smaller columns, where set up for extracting Sm and Nd from low-REE materials. As shown in Fig. 3a, the calibration showed the efficiency of the small columns for the separation of the REEs, using the Bio-Rad AG50W-X8 resin. The resolution of the secondary column (Fig. 3b) was also very good for separation of Sm-Nd, Ce-Nd, and Sm-Gd.

Fig. 3a
- Columns calibration for minerals analysis: REEs elution, where was necessary the concentration correction from blank value obtained in ICP/AES for Ba element.

Fig. 3b
- Columns calibration for minerals analysis: Sm and Nd separation.

REE Separation (Primary Column)

The column was packed with cation resin to a height of 7 cm (column of i.d. = 5 mm and height of 10 cm). The flow speed was set at ca. 1 mL/10 min. 250 L of sample were added and washed with three times 250 L of 2.5N HCl. 7 mL of 2.5N HCl were discarded and the REE fraction comes out in 5 mL of 6N HCl. The column was regenerated with 15 mL of 6N HCl. Satisfactory results have also been obtained working with a larger aliquot of sample (500 L).

Sm-Nd Separation

The column was packed with the LN-spec resin to a height of 7 cm ( 100 mg) and 0.5 cm of anionic resin Bio-Rad 200-400 mesh was added on top. The flow speed was set at 1 mL/50 min. 100 L of sample in 0.18N HCl was added and washed three times with the same amount of 0.18N HCl. The elution was carried out (Fig. 3b) with 0.18N HCl. The first 6 mL were discarded and Nd was extracted in 3 mL of 0.3N HCl. Elution of 2 mL of 0.3N HCl, followed and Sm is extracted in 3 mL of 0.4N HCl. The column is regenerated with 5 mL of 6N HCl.

PRELIMINARY STUDIES

Partition Coefficient and Separation Factor

The selectivity (Table I) of the liquid HDEHP, using a fine graned (270-150 mesh) powdered teflon as support, showed better efficiency than using a coarse powder (60-40 mesh), due to the increase in the ion exchange capacity of the resin. In Fig. 4a, the ion exchange reverse behaviour of HDEHP resin is observed, where the light REEs are first eluted. For the separation of Ba-La-Ce-Pr-Nd, the best concentration of HCl to be used proved to be 0.18N. This has been already observed empirically during the calibration and later on with the determination of the partition coefficient (Fig. 4b). For the separation of Sm-Eu-Gd the best concentration of HCl proved to be between 0.35 and 0.4N (Fig. 4c and d). In this concentration, a large separation factor (ratio between the coefficients of distribution of these elements) is observed. The separation of Nd-Sm happens in concentrations 0.3N (Fig. 4e and f). The use of stronger acids will result in the elution of some of the Sm into the Nd fraction.

Fig. 4
- Determination of lanthanides partition coefficients.

RESULTS AND DISCUSSION

ANALYTICAL PROCEDURE (MASS SPECTROMETRY)

The fraction collected in the secondary column is evaporated with 2 drops of 0.025N HPO. The residue is dissolved in 1 L of 5 distilled HNO loaded onto a Re filament of double filament assembly. The mass spectrometer used was a Finnigan MAT 262 with 7 collectors and the analyses have been accomplished in static mode. The ¹⁴³Nd/¹⁴⁴Nd ratio was normalised using Nd/¹⁴⁴Nd = 0.7219 and the decay constant used was the value revised by Lugmair & Marti (1978) of /y. The external precision (Table II) for ¹⁴³Nd/¹⁴⁴Nd ratios obtained for the different rock standards used varied between 0.0006-0.0016% and the analytical uncertainty for Sm/¹⁴⁴Nd ratio was smaller than 0.19%.

ANALYTIC CONTROL

International rock standards with very well-known Sm and Nd concentrations and Nd isotopic composition were analyzed. The analyses of these standards were necessary to test the reproducibility of the data and mainly to evaluate the reliability of the methodology in rocks of unknown composition. The standards used (Table III) were: BCR-1 (Ballast-USGS), JB3 (Basalt-GSJ), BHVO-1 (Basalt Hawaiian-USGS), JG2 (Granite-GSJ) and La Jolla.

The rock standard most frequently used for interlaboratorial comparison is the BCR-1 (Table IV). Therefore, some analyses of this standard were carried out during this study. They revealed an average value for the ¹⁴³Nd/¹⁴⁴Nd ratio of 0.512632±2 (1, n=5). Concentration of Nd and Sm, were 28.73 ppm and 6.66 ppm respectively being in close agreement with the data obtained in other laboratories (Table V).

The BCR-1 standard, that has been used for so many years, is not available anymore. Therefore, we also used the BHVO-1 standard (Table IV). However, because BHVO-1 is only a recent rock standard, not much data from other laboratories are available in the literature.

Nevertheless, results for BCR-1, as well as for BHVO-1, presented good precision and accuracy, with the values being comparable to the recommended values.

The results for JB-3 and JG-2 were used in the preliminary evaluation of the method. The results obtained for standard JB-3 (a basalt) (Table IV) were satisfactory, presenting good precision, although the Sm and Nd concentrations were consistently 2% below the expected value. The concentrations results for JG-2 (Table IV) showed much greater scatter around the average, showing low precision for the final mean value. This value, however, is still statistically the same as the recommended value. One interpretation for the low precision of the data obtained for JG2 is that the standard is not as homogeneous (regarding the REE) as the other three rocks standards. This is only to be expect, because JG2 is a granite standard.

The data for the La Jolla standard in this study tended to be somewhat lower (Table IV) than the recommended value of 0.511860 (USGS).The average value of 0.511835±14 (1) obtained is, however, statistically the same as the recommended if 2 uncertainties are considered.

The average value obtained for the La Jolla standard is comparable with the values obtained in other laboratories (Table V). Our mean value of 0.511835±0.000014 is statistically the same as the expected value of 0.511850 (average of all laboratories).

Nd procedure blanks (Table VI) decreased from 385 pg in the beginning of this study to ca. 74 pg towards the end. Nowadays these blanks are commonly around 30 pg. Blanks tend to be smaller when dissolution is carried out in Savillex® capsules.

The Nd total blanks observed in Geochronology laboratory of the UnB is within the range of values obtained in other laboratories of the world (Table VII and Fig. 5). As shown in Table VI the LN-Spec resin contribute little to the total blank indicating that the largest contribution for the blank is the memory effect in the dissolution vessels, as well as the reagents.

Fig. 5
- Interlaboratorial comparison of the experimental blanks.

ISOBARIC INTERFERENCE FOR Sm AND Nd

Samarium

CeO, BaO (Table VIII) are isobaric interferents with Sm. These interferences can be suppressed by the average discharge due to the low ionization potential of these species, while the emission of the Gd is inhibited by its high ionisation potential. In this study it was observed that the signal of BaO is reduced to negligible proportions during the analysis of Sm and its main contribution, as BaO, will only interfere with masses 154 and 155 of Sm, not representing therefore any important interference. Gd was found in inexpressive amounts, as shown in Fig. 6. The amount of Gd is very small and Gd does not appear in the mass scan. To avoid any possible interference of Gd with Sm, used for the concentration calculations, we carried out an evaluation of the amount of Sm collected in the chromatographic column (Fig. 6 and 7). Maximum contribution of the mass 155 and detection of the mass 160 is observed when Sm is collected in 4 mL of 0.5N HCl, indicating presence of Gd and/or the presence of oxide species as the ¹⁴⁴NdO or even ¹⁴⁴SmO (Fig. 7). In the 3 mL Sm fraction an insignificant amount of the mass 155 is present, which is probably due only to the contribution of the La oxide (La present in the scan). It is observed that, even collecting the Sm fraction in of 4 mL of eluent, the contribution of the isotope 160 of Gd is insignificant, being smaller than 5 mV, what means a contribution smaller than 0.05 mV of Gd, being therefore, negligible.

Fig. 6 - Interference of Gd on Sm. Increased scale, with 2.2 volts for ¹⁴⁹Sm.

Fig. 7 - Mass interference for Sm. A - increased scale, B - with 2.6 volts for ¹⁴⁹Sm.

Neodymium

The interference (Table IX) of BaO is trivial. Most of Ba is vaporized before the Nd analysis. Additionally, the natural abundance of the interfering masses (Ba and Ba) are low (0.11% and 2.42% respectively). Ce interferes (Table IX) with Nd, however, due to the difficulty in separating Ce of Nd totally, it was preferred to use mass 146 as the reference isotope for the fractionation and isotopic dilution calculations. Previous studies have reported the presence of Ce as an important factor causing instability of the ion beam. In this study even when present in great amounts, little instability is observed in the beam. This is well displayed in Fig. 8 which shows that presence of Ce in the Nd fraction is incapable of generating beam instability.

Fig. 8
- Mass interference for Nd. Increased scale, with 2.2 volts for ¹⁴²Nd.

Other isotope present during the analysis of Nd is Pr, but its presence does not represent isobaric interference in the metal form in spite of this. Its interference only happens when Nd is analyzed in the oxide form.

CONCLUSIONS

The improved chemical extraction used in this study following the preliminary determination of the partition coefficient of REEs in the HDEHP resin uses the best possible conditions for extraction of Sm and Nd. The efficiency of the chemical separation appears in the spectrometric analysis where interferences with other elements are kept to a minimum. In the mass spectrometry the presence of Ce and mainly Pr in the Nd fraction was observed. There is absolutely no isobaric interference between Sm and Nd using this procedure. In the Sm fraction there are detectable amounts of Eu, but this does not represent a problem, because its isotope do not interfere with the determination of the Sm isotopic ratios. The main isobaric interference of Sm, Gd, is not detected. Sm and Nd concentrations obtained for the JB3 and BCR-1 rock standards show good accuracy and precision, and isotopic ratio of ¹⁴³Nd/¹⁴⁴Nd for BCR-1 and La Jolla are comparable to the values obtained in other laboratories, demonstrating the reliability of the methodology used at the University of Brasília.

ACKNOWLEDGEMENTS

The authors thank CAPES and to CNPq, for the financial support. The geochemistry laboratory of the University of Brasília is also acknowledged for allowing the analyses of REEs by ICP/AES.

APPENDIX

Notation:

n: normal element

s: spike

i: individual any isotope

j: reference isotope (Nd-146; Sm-152)

u: primary isotope (Nd-150; Sm-149)

v: secondary isotope (Nd-144; Sm-147)

A: atomic mass

iA: atomic mass of an isotope

An: atomic mass of a normal element

As: atomic mass of a spike

W: mass in grams

P: nº of atoms

C: conc. in g/mL

F: atomic fraction

Condensed Notation:

R: ratio of the spike

R: ratio of the normal element

R: mix (spike + normal)

: difference among atomic mass of uAjA; vAjA; iAjA

1. CALCULATION OF THE ATOMIC FRACTION

(1)

2. REPRESENTATION OF THE CALCULATION OF THE ATOMIC MASS:

(2)

3. CALCULATION OF THE CONCENTRATIONS:

no. of moles = mass of the element/A

mass of the element = C(g/g) W (mass in g)

(3)

Using the equations (1) and (2) and simplifying the equation above and rearranging for Cn(g/g):

(4)

Calculation of Nd Concentration

Using the equations mentioned, for a mixed spike of Sm and Nd enriched in Nd (used in the laboratory of geochronology of UnB), we have:

where:

= concentration Nd in the spike = 0.01691492 mols/g

= atomic mass of Nd (144.24 mol/g)

= natural abundance of Nd = 5.6251% (Russ et al. 1971 and Wasserburg et al. 1981)

where:

= (146/150)m = measured in the spectrometer and corrected for mass fractionation.

= (146/150) of the spike = 0.00464026 (calculated from Table II)

= (146/150) natural = 3.05352835 (calculated from Table I - Wasserburg et al. 1981)

Calculation of Sm Concentration

For a mixed spike of Sm and Nd enriched in Sm:

where:

= (147/149) measured in the spectrometer and corrected for mass fractionation

= (147/149) in the spike = 0.0033163 (calculated from Table V)

= (147/149) natural = 1.088396 (calculated from Table IV - Wasserburg et al. 1981)

= concentration of the Sm in the spike = 0.01334888 mols/g

= 150.35 mol/g = natural abundance of the Sm = 13.8504%

4. CORRECTION FOR MASS FRACTIONATION

Thermal ionisation sources, involving the evaporation of the sample starting from a warm filament is subject to the effect of mass fractionation (Potts 1987).

The exact mathematical form of the fractionation law, that describes the instrumental mass fractionation by thermal ionisation is not very well known. The isotope chosen for the correction of the mass fractionation should have great mass difference and their ratio should be also relatively a close to the unit to minimize uncertainties. For Nd the best choice is Nd/Nd and the second best is Nd/Nd (Wasserburg et al. 1981). The factor of fractionation of the isotope of Nd for unit of atomic mass, it is defined as (Wasserburg et al. 1981):

(5)

(6)

(7)

For cases where fractionation is small, these three different laws supply the same corrected values for the required accuracy. However, for cases in which the fractionation is important, each law will supply a different value for the corrected values depending on the choice of the isotope (u,v) used to calculate the correction.

For Nd and presumably also for Sm, the law of exponential fractionation seems to be better to correct the instrumental fractionation than the linear or power law. Therefore, the use of linear or power laws can introduce significant errors in the ratio ¹⁴³Nd/¹⁴⁴Nd, and this only happens when running a highly fractional analysis. This effect can be minimised by the choice of a different pair of isotope for the normalisation. When Nd/Nd is used the effect in ¹⁴³Nd/¹⁴⁴Nd is insignificant; however, for this normalisation, significant errors can be introduced in Nd/¹⁴⁴Nd. Also when we compare data from different laboratories that normalise in a different way, the use of the linear and power laws introduce small, but significant errors. If the data collected have a small fractionation , the choice of the fractionation law is not necessary.

The fractionation law was suggested in Russell et al. (1978) for the analysis of Ca and that also used the Rayleigh fractionation law.

(8)

that corresponds to the equation of the Linear law. Solving for f (Boelrijk 1968):

(9)

Nd isotope - Application in the UnB Laboratory

Reference: 146

Primary: 150

Secondary: 144

Linear law

where:

5. DETERMINATION OF THE RATIO ¹⁴³Nd/¹⁴⁴Nd:

(10)

Isotope of Sm - Application in the Laboratory of UnB

Reference: 152

Primary: 149

Secondary: 147

Linear law

where:

The ratio (used for calculation of the concentration)

6. DETERMINATION OF THE RATIO Sm/¹⁴⁴Nd:

(11)

Using the equation (2):

Using the values of the tables I, IV and VII:

7. TABLES OF USED DATA

The used data for isotopic dilution calculations and Mass Fractionation, are shown in Tables I to VII.

8. CALCULATION OF THE AMOUNT OF SPIKE TO BE MIXED WITH THE SAMPLE

A correctly spiked mixture should have the / ratio close to 1:

Spike

Enriched in = 0.01691492 moles/g =[Ndspike]moles atomic A (mass of the isotope 150 of Nd) using data on Table VII:

=0.01691492 149.9209 = 2.5359 g/mL

Sample

(16)

The amount of spike is:

(17)

where, = weight of the sample (mg) and = weight of the spike (mg).

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Publication Dates

• Publication in this collection
  07 Aug 2000
• Date of issue
  June 2000

History

• Accepted
  09 Nov 1999
• Received
  03 Nov 1998