D-optimal design of fission-track annealing experiments

Fission tracks have been used to estimate time-temperature (t-T) paths of mineral samples of geological interest. Several datasets on annealing rate have been presented, especially for apatite. However, there are still open problems related mainly to chemical composition of apatite and crystallographic orientation of the analyzed crystal sections. Therefore, new annealing data are desirable. However, there are practical limitations (cost and mainly time) on the number of experiments that can be carried out. In this work, a method for optimizing the choice of the experimental conditions of the future experiments is presented, the so-called D-optimal criterion. The D-optimization takes advantage of previous knowledge on the experimental space and the model to be fit, to maximize the information to be obtained from new experiments. It has proved, in other instances, to be suitable for highly non-linear models as the Arrhenius-type equations currently used to fit the fission-track data. A sample example is given, showing that this procedure produces good choices, leading to reliable data fitting.