Simulating feldspar luminescence phenomena using R

Kinetic models have been used extensively for modeling and numerical simulation of luminescence phenomena and dating techniques for various dosimetric materials. Several comprehensive models have been implemented for quartz, which allow simulation of complex sequences of irradiation and thermal/optical events in nature and in the laboratory. In this paper, we present a simple and accurate way of simulating similarly complex sequences in feldspars. We introduce the open-access R scripts Feldspar Simulation Functions (FSF) for kinetic model simulation of luminescence phenomena in feldspars. These R functions offer useful numerical tools to perform luminescence simulations in a user-friendly manner. The mathematical framework of four different types of previously published models is presented in a uniform way, and the models are simulated with FSF. While previously published versions of these four models require numerical integration of the differential equations, the FSF circumvent the need for numerical integration by using accurate summations over the finite range of the model parameters. The simulation process can be understood easily by creating transparent sequences of events consisting of these compact R functions. The key physical concept of the FSF is that irradiation and thermal/optical treatments of feldspars change the distribution of nearest neighbor (NN) distances in donor-acceptor pairs. These changes are described using analytical equations within the four models examined in this paper. The NN distribution at the end of one simulation stage becomes the initial distribution for the next stage in the sequences of events being simulated. Several practical examples and possible applications and extensions of the FSF are discussed.