**ISC SCIENCE** produces isotopic standards and certified reference materials of stable elemental isotopes and isotopically enriched compounds for Isotope Dilution and ICP-MS and/or GC-MS applications.

Methodologies based on Isotope Dilution Analysis (IDA) or Isotope Dilution Mass Spectrometry (IDMS) provide superior accuracy and precision compared to more traditional calibration strategies. IDMS is commonly used for applications where high accuracy and certainty is required, like the certification of Certified Reference Materials (CRM) by National Metrology Institutes. Since IDMS corrects for all possible errors in speciation analysis (no need to correct for recovery and/or extracion/derivatization efficiency, etc.) the application of Isotope Dilution Standards or Isotopic Standards has been widely applied for trace element speciation using ICP-MS and, recently, using GC-MS, a routine technique in testing laboratories.

Isotope Dilution Analysis is based on the modification of the isotopic composition of a sample by the addition of a known amount of an isotopically enriched element or compound generally called tracer or spike. The general concept of isotope dilution can be explained using a simple analogy: How can we determine the large number of white marbles (N_{w}) inside a box?

Although, the simplest way is to count all the marbles it is a very time consuming process and we can commit errors. The best way is to resort of a kind of "dilution" using a known amount of black marbles (N_{b}). The marbles have the same size and properties, the only difference between the white and the black marbles is their colour, which allows us to apply the concept of "dilution" to determine the number of white marbles in the in the box. For that purpose, the black marbles are added to the white marbles in the box. Once black and white marbles are mixed forming a homogenous mixture, a sample of the mixture is taken and the white (W) and black (B) marbles are counted, obtaining this way the relation shown in the figure.

If another sample is taken out of the box, a different number of white (W) and black (B) marbles could be obtained, though the relation W/B will remain the same. The total number of white marbles in the initial sample can be determined according to the following equation:

N_{w}= N_{b}(W/B)

This is the basic concept of isotope dilution analysis that uses the existence of isotopes of the elements and the isotope ratio measurements to quantify elements or compounds with very high accuracy and precision. Isotope dilution analysis provides several unique advantages in relation to classical approaches and is considered a primary method directly traceable to the International System of Units (SI).

The elemental analysis by isotope dilution is based on the intentional modification of the isotopic abundances of the element to be determined in the sample though the addition of a known amount of an enriched isotope of the same element (tracer). The majority of the elements of the periodic table possess more than one isotope, therefore they can be determined by this methodology.

If we consider the number of moles of a poly-isotopic element present in a sample N_{s} and the number of moles of the same element in the tracer N_{t} added to the sample, the number of moles of the element in the mixture N_{m} is given by:

N_{m} = N_{s} + N_{t}

In the same way, we can establish mass balances for the isotopes a and b:

N_{m}^{a} = N_{s}^{a} + N_{t}^{a}

N_{m}^{b} = N_{s}^{b} + N_{t}^{b}

If we divide the two equations the isotope ratio of the isotopes (a/b) in the mixture (R_{m}) can be obtained. When taken into account the abundances of the isotopes a and b in the sample (A_{s}^{a} and A_{s}^{b}) and in the tracer (A_{t}^{a} and A_{t}^{b}), the isotope ratio can be expressed as:

N_{m}^{a} N_{s}^{a} + N_{t}^{a} N_{s}A_{s}^{a} + N_{t}A_{t}^{a}

R_{m} = ----- = ----------- = -----------------

N_{m}^{b} N_{s}^{b} + N_{t}^{b} N_{s}A_{s}^{b} + N_{t}A_{t}^{b}

where

N_{s}^{a} = N_{s}A_{s}^{a}; N_{t}^{a} = N_{t}A_{t}^{a}

N_{s}^{b} = N_{s}A_{s}^{b}; N_{t}^{b} = N_{t}A_{t}^{b}

Rearranging for N_{s} we obtain:

R_{m}A_{t}^{b} - A_{t}^{a}

N_{s} = N_{t} ---------------

A_{s}^{a} - R_{m}A_{s}^{b}

This equation expresses the number of moles of the element in the sample as a function of the number of moles of the tracer added and the abundances of both, as well as the measured isotope ratio. If we define R_{s} and R_{t} as the isotope ratio of the isotope b/a and a/b for the sample and the tracer, respectively, the number of moles of the element in the initial sample is given by:

A_{t}^{b} R_{m}-R_{t}

N_{s} = N_{t} ---- ---------

A_{s}^{a} 1-R_{m}R_{s}

This equation can be transformed as a function of the analyte concentration considering the masses of the sample and the tracer that were taken, ms and mt; the atomic weights of the element in the sample and in the tracer, respectively, M_{s} and M_{t}. By substitution, the final isotope dilution equation is obtained:

m_{t} M_{s} A_{t}^{b} R_{m} - R_{t}

C_{s} = C_{t} ----- ------ ------ ----------

m_{s} M_{t} A_{s}^{a} 1 - R_{m}R_{s}

In this equation the concentration of the element in the initial sample C_{s} can be determined directly by measuring just the isotope ratio in the mixture R_{m}, since all other parameters of the equation are known or measurable. If the element has natural isotopic composition the values M_{s}, A_{s}^{a} and R_{s} can be obtained from the IUPAC tables of isotopic composition and atomic weights of the elements.

Isotope dilution analysis provides several advantages compared to other analytical techniques that use methodological calibrations. As can be seen in the equation, the isotope dilution equation does not contain any parameters that are dependant of the instrumental sensitivity, therefore posible factors that affect the instrument's sensitivity like signal drift or matrix effects don't affect the final result. Further, once sample and tracer have formed a homogeneous mixture, any loss of the sample during sample preparation does not change the final result, since any aliquot of the sample will have the same R_{m} during the whole process.

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