Luminescence

In this chapter we provide detailed R codes which show how researchers can analyze and model their experimental TL data. We provide R codes for the initial rise method and the method of various heating rates, which allow evaluation of both the activation energy E and the frequency factor s. We present R codes for numerically integrating the simple one trap one recombination model (OTOR), as well as for numerically integrating the equations for first, second, and general order kinetics using R. We discuss the general one trap (GOT) differential equation and its analytical solution, which is based on the Lambert W function. Several examples are given for using computerized glow curve deconvolution analysis (CGCD) for single-peak and multiple-peak TL glow curves, based on the R-packages tgcd and the Lambert W function. Specific examples are given of using the new R package RLumCarlo, to simulate TL glow curves with different kinetic parameters. The chapter concludes with a list of recommended experimental protocols, which experimentalists can apply when studying TL signals.

In this chapter we provide detailed R codes that show how researchers can analyze and model their experimental continuous wave OSL (CW-OSL) signals and linearly modulated OSL (LM-OSL) signals. We present detailed examples for computerized analysis of OSL experimental data, using the R packages Luminescence and numOSL, and how to extract the relevant optical cross sections. On the modeling side, we present the GOT equation derived from the OTOR model, show how this equation can be integrated numerically using R, and compare with the analytical solutions for OSL, which are based on the Lambert Wfunction. We show how to transform the shapeless experimental CW-OSL signals into peak-shaped LM-OSL signals and present several examples of using the R package RLumCarlo to simulate OSL signals. The chapter concludes with a list of recommended protocols for analyzing OSL data in the laboratory.

In this chapter we discuss theoretical and experimental aspects of the dose response of dosimetric materials, and use analytical equations to fit experimental data. We define the superlinearity index g(D), and the supralinearity index f(D), and discuss various functions commonly used to describe shape of dose response curves in TL, OSL, OA, and ESR signals: the saturating exponential, double saturating exponential, single exponential plus linear, and the recently derived equation using the Lambert W function. We show how to numerically integrate the equations for the irradiation stage in the OTOR model, and compare with the analytical solution based on the LambertW function. Several detailed R codes are given of fitting experimental data ESR, TL, OSL data, including situations with superlinear dose response. We simulate experiments in which the sample temperature is variable during the irradiation process, and which may affect the dose response of the material. We discuss superlinear dose response as the result of competition between two electron traps during the irradiation, and present experimental data analysis using the new analytical Pagonis–Kitis–Chen (PKC) equation which describes superlinearity effects. This chapter will conclude with an overview of the analytical dose response equations based on the Lambert function, and with a discussion of the importance of the Lambert function in the description of luminescence phenomena.

In this chapter we discuss experimental data and models for time-resolved optically and infrared stimulated luminescence (TR-OSL, TR-IRSL).These techniques can help researchers understand the luminescence mechanisms involved in dosimetric materials. We show how to use R in order to extract the luminescence lifetimes from TR experimental data and show how to analyze the temperature dependence of luminescence lifetimes and luminescence intensity. Specific R codes are provided for TR experiments in quartz and how they can be analyzed with R to obtain the thermal quenching parameters W and C, based on the Mott–Seitz competition mechanism. We show how to analyze TR-OSL signals from delocalized transitions and also TR-IRSL signals involving localized transitions in feldspars involving quantum tunneling. This chapter concludes with the presentation of a TR-photoluminescence (TR-PL) model for the important dosimetric material Al₂O₃:C.

In this chapter we consider the different types of quantum tunneling localized transition (TLT) models. We describe four different types of TLT models: ground state tunneling (GST) model, irradiation ground state tunneling (IGST) model, excited state tunneling (EST) model, and thermally assisted excited state tunneling (TA-EST) model. We provide R codes for exploring the properties of each model, discuss their physical principles, and code approximate analytical solutions to the differential equations describing each model. R codes are provided for simulating the nearest neighbor distribution in a random distribution of defects in a solid and also provide an example of analyzing experimental data to obtain the g-factor for the anomalous fading (AF) phenomenon. Additional R codes simulate simultaneous irradiation and tunneling, and excited state tunneling phenomena. We show how to analyze experimental TL and OSL data for freshly irradiated samples, using the analytical Kitis–Pagonis equations KP-TL and KP-CW. Finally, we present the thermally assisted excited state model used in low temperature thermochronometry studies and show how quantum tunneling phenomena can be simulated using the TUN functions in the package RLumCarlo.

In this chapter we study two localized models found in the luminescence literature, the localized transition model (LT) and the semilocalized transitions model (SLT). We provide R codes for numerically solving the differential equations for the LT model, and compare the solution with the analytical equations involving the Lambert W function. Several examples are presented using the R package RLumCarlo to simulate these types of localized transition phenomena. We present R codes for the important hybrid SLT model developed by Mandowski, which can be used to explain the anomalous heating rate effect observed in several dosimetric materials. Finally, the chapter concludes with the presentation of a simplified form of the SLT model, developed by Pagonis et al.

In this chapter we discuss fixed time interval MC simulations of luminescence signals produced by localized transitions in the TLT and LT models. Examples of R codes are provided for TL, CW-IRSL, and LM-IRSL signals in the excited state tunneling (EST) model, and the MC results are compared with the analytical Kitis–Pagonis equations (KP-CW, KP-TL). The R codes also provide estimates for the stochastic coefficients of variation CV% for a variety of processes. This chapter concludes with a MC simulation for the LT model.

While previous chapters looked at examples of MC methods with a fixed time interval, in this chapter we present several examples of kinetic Monte Carlo (KMC) methods. KMC methods are based on the concept that the variable time intervals between random events follow an exponential distribution. R codes are provided here for KMC methods applied to luminescence signals as stochastic birth and death processes. The chapter concludes with a different example of the KMC method, which describes quantum tunneling processes and the anomalous fading effect from a microscopic point of view. We compare the stochastic KMC results and the corresponding CV% uncertainties with the solution of the corresponding deterministic differential equation.

This chapter presents several empirical comprehensive models that were developed in order to explain complex luminescence mechanisms and phenomena in quartz. We show detailed R codes for the Baiiley2001 and the Pagonis2008 quartz models, by using the R programs KMS developed by Peng and Pagonis, and also using the R package RlumModel by Friedrich et al. We show how to simulate the history of natural quartz samples, and how to modify the models by changing one or more of the original model parameters. R codes are provided for studying the phenomena of thermal quenching, for simulating the dose response of TL and OSL signals and also for the superlinear dose response in quartz. We show how to simulate the important phenomena of phototransfer, predose effect and thermal transfer of holes, pulse annealing, and the SAR protocol in quartz. This chapter concludes with several examples from the extensive R package RLumModel.

In this chapter we provide R codes for four different models previously developed for feldspars, apatites, and other materials exhibiting quantum tunneling phenomena. These are the ground state tunneling (GST) model, irradiation GST (IGST) model, excited state tunneling (EST) model, and thermally assisted tunneling (TA-EST) model. We demonstrate appropriate R functions that can simulate a wide variety of processes in feldspars, for both natural and laboratory irradiated samples. We present specialized codes for analyzing CW-IRSL and TL signals from freshly irradiated samples, as well as for simulating a variety of multiple stage experiments, involving thermal and optical pretreatments of samples in the laboratory. The chapter concludes with several R examples for the TA-EST model, which can be used for low temperature thermochronology studies.