A simple shape-free model for pore-size estimation with positron annihilation lifetime spectroscopy

Positron annihilation lifetime spectroscopy is one of the methods for estimating pore size in insulating materials. We present a shape-free model to be used conveniently for such analysis. A basic model in classical picture is modified by introducing a parameter corresponding to an effective size of the positronium (Ps). This parameter is adjusted so that its Ps-lifetime to pore-size relation merges smoothly with that of the well-established Tao-Eldrup model (with modification involving the intrinsic Ps annihilation rate) applicable to very small pores. The combined model, i.e., modified Tao-Eldrup model for smaller pores and the modified classical model for larger pores, agrees surprisingly well with the quantum-mechanics based extended Tao-Eldrup model, which deals with Ps trapped in and thermally equilibrium with a rectangular pore.