A proposal for calibration with locally varying references

Local Analysis aims at quantifying the local material composition at small measurement location, in larger heterogeneous specimen. In many cases it is technically impossible to produce homogeneous samples of that material classes to provide homogeneous standards or reference materials. The corresponding reasons are manifold, for example not reaching thermodynamic equilibrium, kinetic delays in crystallization, exsolution in solid solutions or immiscibility in glass-forming melts.

We therefore propose a class of methods to be coined “local calibration”, which would allow to establish traceability of local chemical measurements based on references consisting of heterogeneous reference specimen along with a new kind of description/certification for local analytical methods. Such a certification would not only define a single reference value, minimum sample size and accuracy, but describe in more detail, how the material can be used as reference, Such a description could for instance provide a measurement mask or rule ensuring that only certain minerals are used in reference measurements, or it could include a description of the local concentrations in a specimen with locally varying concentrations. The kinds of descriptions would depend on the type of heterogeneity of the reference specimen, the characteristics of the local measurement procedure it is certified for (like e.g. the interaction volume, or whether the method is destructive) and on technologies available for the description process. The methodology includes a validation procedure ensuring traceability.

The methodology is based on a simple observation: Local analysis only depends on a local material portion, and will deliver measurement values dependent of the local composition irrespective of a larger scale heterogeneity or homogeneity of the larger specimen. It is thus sufficient to provide an accurate and traceable value for the measurements which will be actually done during the use of the reference specimen. Depending on the type of heterogeneity this is however possible through various statistical and analytical strategies, such as, e.g. establishing a local map using a calibrated reference technique if such a technique is available, providing a geostatistical interpolation in case of slowly varying local concentration gradients, or by physical modeling the source of concentration differences (e.g. in case of a growth gradient). In each case all aspects of such a description can be checked statistically, based on control measurements.