# Standard Addition, Internal Standardization and Isotope Dilution

## Overview

Part 11 of this series is a continuation of discussions around the recommendations made in part 10. Please reference Part 10: Calibration Curves before you proceed.

**Discussion (c and d)** - For the sake of convenience, recommendations (c) and (d) are reprinted from Part 10 as follows:

**Recommendation (c)** - With unknown sample matrices, matching is not possible and is most accurately dealt with using the technique of standard additions. However, this approach is slow as compared to the calibration curve technique with the use of internal standardization.

**Recommendation (d)** - The use of internal standardization is very effective in many cases but may introduce--or not correct for--all errors. This statement does not apply to isotope dilution ICP-MS that is considered to be a primary analytical technique.

Matrix effects are arguably the subtlest danger to the ICP-OES analyst. Slight differences in the matrix can cause a considerable systematic error. The most common calibration technique options for ICP measurements are *calibration curve* and *standard additions*.

## Standard Additions

The technique of standard additions is used when the matrix is quite variable and/or when an internal standard that corrects for plasma related effects couldn't be found. This technique is also useful in confirming the ability of an internal standard calibration curve technique to correct for both nebulizer and plasma related effects (see part 10 of this series for more on nebulizer and plasma related matrix effects). The following considerations may prove useful in performing the technique of standard additions:

- Split the analytical (sample) solution accurately. For example, if the final sample solution is made to 100.00 grams, then remove exactly 50.00 grams of solution to a separate clean container for spiking.
- The technique of standard additions requires a linear response. It is therefore important to work within the linear working range for each analyte.
- It is beneficial to perform a quick semi-quantitative analysis of the unknown to estimate analyte levels so that the analyst can spike the unknown solution with a concentrate of the analyte(s) of interest to levels of between2x
_{?}and 3x_{?}where x_{?}represents the unknown concentration(s) of the analyte(s) of interest. - Many analysts prefer to make more than one spiked level (i.e., 2x
_{?}, 3x_{?}, 4x_{?}, and 5x_{?}). As with all techniques, a primary concern is in making an accurate spiked addition. For ICP, an additional concern is drift. The objective is to make an**accurate measurement**. Rather than making multiple spiked additions where drift is given more ground to introduce error, it is suggested that the analyst measure the sample along with a single spiked sample several times to account for drift. A reasonable measurement sequence would be:**blank → sample → blank → spiked sample → blank → sample → blank → spiked sample → blank → sample → blank**—where an average of all measurements is taken for the final calculation. The above analysis sequence assumes linear drift that should be confirmed before acceptance of the data.

- Attempt to keep the spiking volumes low. For example, a spike of 100 µL to a 50.00 gram sample aliquot represents a 0.2% relative error. If larger spiking aliquots are required then an equal volume of 18 MO water should be added to the unspiked sample portion to cancel out volume dilution errors.
- The technique of standard additions assumes that the instrumental response is described by the equation of a straight line with x,y coordinates of 0,0 as follows:

**(1)** Y_{I} = mx_{?}

where Y_{I} = intensity of the sample,

m = slope,

and x_{?} = concentration of the unknown analyte

When a spike addition is made the equation becomes:**(2)** Y_{k} = m(x_{?} + x_{s}) = mx_{?} + mx_{s}

Where x_{s} = the concentration contribution from the spike addition to the analyte concentration

and Y_{k} = intensity for the spiked sample

- Note that the above equation (1) relating intensity (Y) to concentration (x) requires that the intensity is zero at an analyte concentration of zero. It is therefore necessary that the signal intensities be background corrected.
- The analyte concentration is determined as follows:

Subtract the intensity of the spiked from the unspiked sample solution and divide this by the concentration of the analyte spike to calculate the slope (m)

Y_{k} - Y_{I} = mx_{?} + mx_{s} - mx_{?} = mx_{s}

(Y_{k} - Y_{I}) / x_{s} = m

Substitute the value for m into equation (1) along with the intensity (Y_{I}) to calculate the unknown analyte concentration (x_{?})

The technique of standard additions offers the best possible solution to matrix interference through plasma related effects. The technique it requires an accurate background correction of the analytical signal intensities and does not account for instrument drift. For unknown matrices, it may well be the fastest approach. When using standard additions on unknown matrices, it is possible to have severe spectral and background correction problems. It is cautioned here that at least two spectral lines should be used and the spectral region carefully scanned and studied.

## Internal Standardization

The calibration curve technique is the most popular calibration technique. If the sample matrices are known and consistent then matrix matching the calibration standards to the samples is an excellent option. Even when matrix matching is an option, many analysts still use an internal standard. It is suggested that the analyst consider the following questions before using an internal standard:

- Is the internal standard (IS) element compatible with your matrix? (Avoid using rare earths in fluoride matrices.)
- Are there any possible spectral interferences upon the IS line?
- Is the concentration of the IS sufficient to give a good signal to noise ratio?
- Can your sample possibly contain the IS element as a natural component?
- Is the IS clean? Are the trace impurities reported on the certificate of analysis?
- Is your method of addition of the IS very precise? Is the same amount added precisely to all standards, blanks, and samples?
- Do you always use the same lot of IS for the standards and samples? (Using the same lot is very important.)
- If your plasma temperature were to go up or down, is the IS likely to follow the same pattern of intensity change as the analyte? This is where many IS problems occur (i.e., - an IS with the same plasma / temperature behavior as the analyte is difficult [at best] to find for each analyte while avoiding other issues listed above).

As discussed in the last part of this series, the matrix can influence the plasma as well as the nebulizer. Internal standardization is very effective in correcting for nebulizer related effects and *may be* effective for correcting plasma related effects. It is obviously important that the matrix effect influence both the internal standard to the same extent as the analyte. This should be the case for nebulizer related effects but it may not be so for plasma related effects where the matrix influence is related to the excitation potential of the emission line (as discussed in Part 10). It may be difficult to find an internal standard that has a similar excitation potential as the analyte in measurements where several analytes are involved. The analyst is advised to confirm that the matrix influences the internal standard and analyte signal intensities proportionately.

## Isotope Dilution Mass Spectrometry

As discussed in part 10, ICP-MS suffers form matrix related effects upon the nebulizer and the signal intensity (quenching). In addition, even slight deposition on the sampler cone will cause drifting. Due in part to drifting, analysts have chosen to use the calibration curve technique with internal standardization over the technique of standard additions. Although the standard additions technique should work well in theory, the drifting associated with ICP-MS is too pronounced. The use of a ratio technique such as internal standardization is a reasonable compromise with the understanding that the internal standard is not influenced to exactly the same degree as the analyte signal. This is due to mass dependence. The internal standards commonly used are only used over relatively narrow mass ranges making the use of multiple internal standard elements required for broad mass range applications. The most common internal standard elements listed from low to high mass are ^{6}Li (isotope 6 enriched), Sc, Y, In, Tb and Bi.

ICP-MS has the unique capability of using an enriched isotope of the element of interest as the internal standard. This technique, which is known as **isotope dilution mass spectrometry (IDMS)**, has been known for nearly 50 years^{1}. IDMS is made possible through the availability of enriched stable isotopes of most of the elements from the electromagnetic separators in Oak Ridge, Tennessee (U.S.A). IDMS is therefore not applicable to monoisotopic elements.

The IDMS technique involves the addition of a known amount of an enriched isotope of the element of interest to the sample. This addition is made prior to sample preparation during which the spiked addition of the enhanced isotope is 'equilibrated' with the sample. By measuring the isotope ratio of the sample and sample + spike isotope addition and knowing the isotopic ratio of the enhanced addition, the sample concentration can be calculated. The entire measurement is based upon ratio measurements of one isotope of the element to another. Drift, quenching and other related matrix effects do not present an interference with IDMS. This technique is considered a *definitive*_{2} method and is well suited and established for the certification of certified reference materials.

IDMS is free from matrix effects (physical interference) but it is not interference-free in that mass interference must still be dealt with (isobaric, MO^{+}, M^{++}, etc.) in addition to correction of the signal intensity for detector dead time and mass bias interference.

To view an example of an IDMS method, reference EPA Method 6800.

1. Hintenberger, H, *Electromagnetically Enriched Isotopes and Mass Spectrometry*, Proceedings Conference, Harwell, (1955): pg 177; Butterworths Scientific Publications, London.

2. *Definitive* is defined as, "A method of exceptional scientific status, which is sufficiently accurate to stand alone in the determination of a given property for the *Certification of a Reference Material*. Such a method must have a firm theoretical foundation so that systematic error is negligible relative to the intended use. Analyte masses (amounts) or concentrations must be measured directly in terms of the base units of measurements, or indirectly related through sound theoretical equations. Definitive methods, together with Certified Reference Materials, are primary means for transferring accuracy -- i.e., establishing traceability.*Traceability* is defined as, "The property of a result or measurement whereby it can be related to appropriate standards, generally international or national standards, through an unbroken chain of comparisons."