4.1. Accuracy and precision
It is clear from the equations presented above that the determination of anE- or L-value is the end result of a number of independent measurements.
Consequently, any error in a single measurement is propagated through the calculation of the labile pool. In the case ofE-value determinations made using a radioisotope, three independent measurements are needed: (1) the total
314 Rebecca E. Hamonet al.
activity of the tracer isotope added to the system, (2) the activity of the isotope in the solution after equilibration, and (3) the total concentration of the element in the equilibrated solution. Activities of the radioisotopes are assessed using standard methods forg- orb-radiation. These analytical techniques are usually both accurate and precise, providing spectral interferences (e.g., inter- ference of65Zn on109Cd) and quenching issues have been accounted for, and if the recorded counts are sufficiently greater than the background levels. Note that appropriate decay correction is also an important consideration, especially for short-lived radioisotopes. The total amount of radioisotope added is usually analyzed in acidified ‘‘blank’’ solutions spiked with the radioisotope, but without the soil. Acidification of the solution is essential to avoid loss of isotope due to sorption to glassware and filters, especially if it is added ‘‘carrier-free’’
whereby the total number of atoms per liter in the spiking solution is very low.
In the case ofL-values, the total amount of radioisotope added is measured either in a digest of the labeled soil (Smolders et al., 1999) or in the stock solution used to spike the soil (Hutchinson et al., 2000). The accuracy/
precision of measurements of the analyte concentration in solutions depends on the analytical technique used and is beyond the scope of this chapter. It is, however, an important consideration in assessing the overall accuracy of a calculated E- or L-value (see Section 4.3). Generally, the use of dilute salt solutions, or a deionized water extract in conjunction with a resin purifi- cation step, both increases the concentration of the analyte in solution (thus improving accuracy) and reduces the problem of colloidal interferences (see Section 4.5).
4.2. Spike-derived artifacts
WhenE- orL-values are determined using stable isotopes, a single instru- ment (usually an ICP-MS) is used for all measurements. In addition to errors due to isobaric interferences (which vary depending on the instrument utilized and are not discussed here), a significant source of uncertainty can arise from the amount of the isotope added. In fact, the decision regarding the amount of added isotope is a balancing act between two contrasting needs: on the one hand, the statistical errors of the measurements are minimized if the number of added spike atoms equals the number of isotopically exchangeable atoms in the sample (Heumann, 1988) but on the other hand, a large amount of added isotope may cause changes in the speciation of the element investigated. Moreover, if a large amount of isotope is added, some of the isotope may undergo precipitation reactions, thereby not participating in isotopic exchange. This violates one of the conditions for isotope dilution (viz ‘‘the isotope introduced in the system has not perturbed the equilibrium of the system’’) and results in an overes- timation of the isotopic exchangeability. Artifacts arising from precipitation of the spike can be tested by examining the effect of an increasing spike
Advances in Isotopic Dilution Techniques in Trace Element Research 315
concentration on measured E-values; if all of the assumptions of isotopic dilution are valid, then theE-value should be independent of the amount of spike added.Figure 3shows the effect of increasing206Pb spike (added at 1, 2, 5, 10, 20, 50, and 100% of total soil Pb) on the determination of the Pb E-value in two soils. The results obtained for Soil 1 show an increasingE- value with increasing amounts of added isotope. This indicates that the E-value is already overestimated at relatively low additions of spike (<2%
total soil Pb), which can be attributed to precipitation of the added spike.
Note that theE-value may also be overestimated in Soil 1 at the lowest spike addition (1% total soil Pb); however, detection limit issues precluded the addition of a lower amount of isotope to assess this. The solubility of Pb in soils is much lower than the solubility of many other metals, and it would be expected that this would be reflected in a relatively small labile pool of Pb as a proportion of the total soil Pb content. In contrast, Degryseet al. (2007) remarked on the high lability of Pb found in their study in comparison to documented lability for other metals, and other studies have similarly reported relatively large values for the labile Pb pool (Table 1). We hypoth- esize that preciselybecausePb solubility in soils is low,E- andL-value results for this element are more likely to be compromised by precipitation arti- facts, resulting in an overestimation of the actual lability, unless great care is taken to prevent this.
Amount of isotope added (mg kg−1)
10,000 1000
100 10
E-value (mg kg−1)
600 800 1000 1200 1400 1600
Soil 1 Soil 2
Figure 3 Lead (Pb)E-values in two soils as a function of increasing amounts of spiked
206Pb (Hamon and Nolan, unpublished data).
316 Rebecca E. Hamonet al.
In contrast, one concern aboutE- or L-values determined using radio- isotopes, discussed at length in the early literature (Tiller et al., 1972), was irreversible binding of the isotope to vacant sites on the soil surface, coined
‘‘isotope fixation’’. This theory was originally proposed to try to explain severe overestimates (i.e., E-value>total soil element) of E-values that were fre- quently observed in soils where theE-values were expected to be low (e.g., in the case of Zn: soils with high pH and low total Zn content). The essence of this theory is that in some circumstances, isotopic exchange is impeded by the existence of vacant binding sites that instantaneously sequester and ‘‘fix’’ the introduced trace atoms, hence circumventing the exchange process because there are no atoms of native element already present at the sites to exchange with. It was thought that this problem was exacerbated by the small number of tracer atoms added duringE-value determination such that a small number of these vacant sites would nonetheless cause a large, positive error in the calcu- latedE-value. Indeed, preequilibrating the soil with carrier (with the aim being to ‘‘saturate’’ any such vacant sites, making them no longer accessible to the added tracer atoms) did yield lowerE-values (Tilleret al., 1972). However, it seems thermodynamically implausible that a system that hosts a measurable (if low) concentration of isotopically exchangeable native element in solution would simultaneously host vacant sites that do not bind the soluble native element already present, but which nevertheless can selectively and irreversibly bind radioisotope or other tracer atoms added in a very small amount.
One exception would be if the chemistry of the added isotope is sufficiently different from the native element that major isotopic discrimination occurs (i.e., violating the condition that ‘‘the introduced isotope behaves exactly as the natural element’’). This seems unlikely for most metals/metalloids that have a high enough atomic mass that a difference of a few neutrons is of little overall significance, though more investigation may be needed (seeSection 4.4).Hamonet al. (2002b)have provided an alternative explanation to account for the results ofTilleret al. (1972)that does not invoke vacant sites. Moreover, other credible candidates that could explain reported overestimates ofE-values determined in high pH or uncontaminated soils include the susceptibility of measurements made in such soils to colloidal interferences (seeSection 4.5), and the fact that any measurement of analytes near their detection limit is inherently subject to analytical difficulties.
Finally, changes in lability can arise if the added spike solution contains components that acidify or otherwise alter the overall sample (Gableret al., 2007).
4.3. Error propagation
Errors in the determination of E- and L-values might arise simply from experimental error, as the values depend on several exacting analyses.
Excepting the early work of Tiller et al. (1972), there have been few
Advances in Isotopic Dilution Techniques in Trace Element Research 317
systematic analyses of sources of error and uncertainty in the determination of E- andL-values. As a simple example, consider the determinations of E- andL-values made byGoodsonet al. (2003)using75Se. The quantifica- tion of the radioisotope involves two separateg-counter measurements, one for the background and one for the sample. Because the net activity is derived from the difference between the sample counts and the background counts, the overall uncertainty is calculated using standard conventions for the propagation of indeterminate errors (Wanget al., 1975):
Stracer ẳ ðs2totalỵs2backgroundị2 ð8ị whereStraceris the absolute uncertainty in the measured net radioactivity (in cpm) andstotalandsbackgroundare the standard deviations for the sample and background measurements, respectively (and typically taken to be the square root of the measured count rate).
The uncertainty in the measurement of the ‘‘cold’’ Se can be estimated from the standard deviation of several replicate readings of a single sample using HVG-AAS, typically about 0.3mg liter1Se in our laboratories (ẳSreference).
Then, becauseE- andL- values are both derived from the quotient of ‘‘cold’’
Se to isotopic tracer, the overall, relative uncertainty is given by
%SrðEorLịẳ Stracer
Se
2
þ Sreference
ẵSe
2
" #2
100 ð9ị
where Se is the measured, background-corrected 75Se activity in cpm and [Se] is the measured solution Se concentration in mg liter1. This uncertainty is depicted inFig. 4for representative values of75Se counting and Se analysis by HVG-AAS as employed byGoodsonet al. (2003). The figure suggests that, to achieve overall accuracies to within 5%, data collection should be restricted to cases where (1) total75Se activity exceeds about 2000 cpm and (2) ‘‘cold’’ Se exceeds about 9mg liter1.
4.4. Uncertainties and sources of error specific toL-value determination
In the calculation ofL-values [Eq. (3)], the elemental content of the seeds should be subtracted from the total metal content of the plant. Similarly, in the case of labile pools determined using different biological systems such as earthworms or snails, the amount of metal in the juvenile invertebrates should be subtracted from the metal present in the organism at the end of the experiment. However, the seed/juvenile contribution is often negligible if the seed/juvenile size is small, and if the plants/invertebrates are allowed to
318 Rebecca E. Hamonet al.
grow to a reasonable size (Tiller and Wassermann, 1972). For instance,Hamon et al. (1997)showed that for the plants in their study, the seed contribution to the total metal content of the shoot could be minimized to<5% if the plants were left to grow for several weeks.Scott-Fordsmandet al. (2004)calculated that the Zn content of juvenile earthworms could lead to a maximum error of 10%.Scheifleret al. (2003)accounted for the initial amount of Cd in snails and the Cd contribution of the food source (lettuce) by subtracting the amount of Cd accumulated in snails grown in an uncontaminated soil from that of snails grown in a contaminated one.Oliveret al. (2006)reported that, under their experimental conditions, seed contribution to CuL-values was not significant when tomato seeds were used because of their small size and small Cu content.
In contrast, when ryegrass was used there was a significant impact on theL- values determined, and they had to be corrected for the seed Cu content. This contribution was determined by germinating the seeds in petri dish for 10 days and measuring the Cu content in the seedling shoots. Therefore, seed contri- bution is not a factor that can be discounteda priori, and care must be taken to avoid overestimation ofL-values due to the seed contribution.
Another consideration in the determination of L-values is possible dis- crimination of the isotopes during uptake. One of the key assumptions of any
Relative error in E- or L-value (%)
Aqueous [Se], mg L-1
75Se activity, cpm
1 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500
0 4 8 12 16 20 24 28 32
3 5 7 9 11 13 15
Figure 4 Relative uncertainty in the calculated E-or L-value as a function of the counting rate for75Se byg-counting and the ‘‘cold’’ Se in solution as determined by HVG-AAS. Background count rate is taken to be constant at 495 cpm. Assumed uncertainty in the HVG-AAS determination of Se is0.3mg liter1.
Advances in Isotopic Dilution Techniques in Trace Element Research 319
L-value determination is that all the isotopes of an element of interest, which are in equilibrium in the labile pool, are taken up and assimilated with equal ease by the organism under study. However,Weisset al. (2005)have reported isotopic discrimination of Zn in higher plants. In particular, they observed a preferential uptake of the lighter 64Zn isotope over66Zn when plants were grown in nutrient solutions. The extent of this discrimination is limited (0.13% to 0.26% per atomic mass unit) and as such would not have a significant effect on the determination of the labile pool, but information in this regard is scarce and more investigation is needed.
One procedural aspect that is extremely important in the determination of correctL-values is the mixing of the isotope with the soil. As we discussed in Section 1of this chapter, one of the fundamental assumptions of the isotopic dilution principle is that the introduced isotope has physically mixed with the entire labile metal pool. This condition is obviously easier to achieve in the determination ofE-values, which is generally conducted using a batch system and dilute slurry (Fig. 1), than forL-values where the isotope has to be manually or mechanically mixed into the soil in which the plants will be grown (Fig. 1).
Because plant roots may only sample an incomplete proportion of the soil (especially in the early stages of growth), any heterogeneity in the distribution of the introduced isotope, as well as the metal present in the soil, will have an effect on theL-values (Hamonet al., 1998). For instance, if the isotope is not homogeneously distributed and the plant roots grow in areas where the introduced isotope is not present, the L-value will be overestimated. The opposite result can occur (L-values underestimated) if the root system grows into areas where the introduced isotope is accumulated. It is therefore impera- tive that the soil used is homogenized and the added isotope is thoroughly mixed with the soil.
The best way to achieve a thorough mixing will depend on the nature of the soil (clay soils are more difficult as they tend to form aggregates when wet) and the isotope used (mechanical mixing, for safety reasons, should be preferred when radioisotopes are used). When a large amount of soil is to be spiked for L-value determinations, adding the isotope diluted in an appro- priate amount of water (rather than using a few microliters of concentrated solution) helps to ensure a more thorough mixing.
4.5. Colloidal interferences
If nonisotopically exchangeable colloidal metals (Mcol) are present in the filtered solutions (Msol), then the unlabeled metal concentrations, and consequently the E-values, are overestimated as can be deduced from the following equations:
E ẳMsol
asol AD<MsolþMcol
asol AD ð10ị
320 Rebecca E. Hamonet al.
As mentioned previously, a resin purification step was developed to remove this interference (Hamon and McLaughlin, 2002; Lombiet al., 2003). Briefly, after equilibration of the isotope with the soil suspension, the liquid phase is separated from the soil by filtration through a 0.45 or 0.2mm filter. An ion exchange resin is used to separate the element of interest (and the isotope) from any nonlabile colloidal forms present in the filtered extract (Fig. 2). The metals and/or metalloids of interest are then eluted from the resin and their concen- tration and radioactivity measured. Colloidal interferences generally increase with increased pH and can lead to overestimations of the labile pool that are very significant. For example, overestimations of up to 60% for Cd, Zn, Cu, and As were found by Lombi et a l. (2003, 2004). The resin purification method also allows additional information to be obtained during the determination of labile pools, specifically, an assessment of the presence of nonisotopically exchangeable metals/metalloids associated with the colloids.
Sinajet al. (1999, 2004)proposed the use of ion chromatography to assess Msol. This method should avoid colloidal interferences but is less sensitive than other analytical techniques. In addition, if Msolis measured using ion chromatography thenasolalso needs to be measured in the eluant obtained by ion chromatography and not on the original solution. Otherwise, the E-values will be most likely underestimated due to relative isotopic enrich- ment of the original solution as a result of isotope sorption to surface exchange sites on any colloids that are present in the original solution.
4.6. Changes in oxidation state
In the case of redox-labile elements such as As, Co, Cr, Fe, Mn, and Se, there is the potential to incur large errors duringE-value determination if the introduced isotope changes redox state during the equilibration period and this is not accounted for (Hamonet al., 2004). In other words, if the isotope changes redox state, and theE-value of the system is determined by the standard procedure of simply measuring the concentration and isotopic activity of the element in solution, hence ignoring the solution-phase speciation of the element and isotope, hidden within the calculated E-value are multiple components (Eq. (11)) and the result of this calculation may be incorrect (Hamonet al., 2004):
PIEẳ Mox1 ỵMox2 aox1 þaox
2
!
ðAox
1þAox
2ị
!
D ð11ị
where PIE is the potentially incorrect E-value; Mox1 and Mox2 are the solution concentrations of the two oxidation states; aox1 and aox2 are the activities of the isotope with two oxidation states in solution;Aox1 and Aox2 equals the total activity,A, initially added to the system; andD, as before, is
Advances in Isotopic Dilution Techniques in Trace Element Research 321
the dilution factor. In contrast, the correct equation for calculating the total E-value (Etot) for an element having two oxidation states can be written as follows (Hamonet al., 2004):
Etot ẳ Mox1 aox
1
Aox1
!
þ Mox2 aox
2
Aox2
!!
D ð12ị
Hamonet al. (2004)observed that the function Etotwill be equal to PIE- value when one of the two oxidation states is not present or, for soils containing appreciable quantities of element in both oxidation states, when theKdfor the two oxidation states are equal. These authors investi- gated changes in As lability in two soils under different redox conditions.
Arsenic exists in two oxidation states, As(V) and As(III), and it can be expected that the Kd for the two states will be very different with As(V) larger than that of As(III) (Smith et al., 1999). Preliminary experiments showed that irrespective of whether it was introduced to the soils as As(V) or As(III), a portion of the isotope converted to the alternate species during the equilibration period. Hence, Hamonet al. (2004) considered that the PIE-value (which to calculate, only requires knowledge of the total amount of isotope added, and the combined solution concentration and activity of cold and radioactive species, respectively) could not be substituted as a measure of Etotin their system. The latter (i.e.,Etot) requires much more information in order to calculate, namely, knowledge of the solution con- centration and activity of cold and radioactive As(V) and solution concen- tration and activity of cold and radioactive As(III) as well theKdof one of the redox species.Hamonet al. (2004)solved this problem by coupling the isotopic dilution technique with a speciation of both the stable and the radioisotope by HPLC-ICP-MS and HPLC-g-counting. In addition, the Kdfor the As(III) species was determined after repeated extractions with 0.1 M NH4H2PO4 followed by HPLC-ICP-MS analysis that enabled assess- ment of the total amount of73As(III) in the system.
However, we have realized that the functionEtotwill also be equal to PIE-value when the specific activities of the species in solution are the same, that is, when:
aox
1
Mox1
ẳ aox
2
Mox2
ð13ị This observation potentially greatly simplifies the determination of Etotin systems with different redox states because if a determination of the solution concentration and activity of the different species shows that their specific activities are the same, then the extractive step to establish theKdof one of
322 Rebecca E. Hamonet al.