Phenomenological model of Aluminum-hole defect formation in sedimentary quartz: Electron Spin Resonance (ESR) study

The mechanism governing the production of the paramagnetic Al-hole centres ([AlO₄/h⁺]⁰) in quartz as function of given dose is of great importance in Electron Spin Resonance (ESR) dating, as the analytical function used to characterise the evolution of this centre with accumulated dose is used to derive the equivalent dose by extrapolation to the abscissa-axis. The single saturating exponential model fails to accurately represent the dose response curve especially at high doses, and consequently, empirical functions, such as a saturating exponential plus a linear term, are widely used in the dating community. Herein, a physical phenomenological model is presented to describe the Al-hole formation under gamma irradiation in sedimentary quartz. We propose that Al-hole centre is formed via the dissociation of the Al centres compensated with alkali ions, generally denoted as [AlO₄/M⁺]⁰ where M⁺ could be Li⁺, Na⁺ or K⁺, as well as by the dissociation of Al compensated with hydrogen ([AlO₄/H⁺]⁰). We further assume then when irradiation moves alkali interstitials away from the aluminium ions, they can be replaced by H⁺ ions beside the conversion to Al-hole centres. By assuming that the rate of the dissociation process is proportional to the concentration of the defects themselves, a sum of saturating exponential functions is obtained for describing the growth of Al-hole with dose. Additionally, the model can be used also for predicting the evolution of the diamagnetic precursors ([AlO₄/M⁺]⁰  and [AlO₄/H⁺]⁰)  with accumulated dose. The model is applied on data obtained on sedimentary quartz specimens of different origins for describing the dose response of the paramagnetic Al-hole ESR signal. We are showing that the signal of this later does not reach full saturation at doses even as high as 250 kGy and can be well represented by two exponential components as predicted by the model. As such, the additional linear term reported by other works when describing the dose response is but a first order approximation of one of the saturating exponential functions.