A theoretical and experimental assessment of systematic errors in nucleation experiments

Abstract

Equations are derived for the fractional underestimate in the number of particles per unit volume, N v , and in nucleation rates, I 0, as obtained by stereological techniques from reflected light microscopy or SEM for typical cases of crystal nucleation in glasses. Three cases are considered: (i) instantaneous heterogeneous nucleation (mondispersed systems of particles); (ii) simultaneous homogeneous nucleation and growth in a single-stage heat treatment (uniform distribution of particles from the critical size to D M, where D M is the largest diameter); (iii) case (ii) with a double heat treatment (uniform size distribution from D M, the smallest diameter, to D M). Comparison with experimental nucleation data for BaO SiO 2 and Na 2O CaO SiO 2 glasses demonstrates that the equations derived predict well the observed underestimations Typical experiments with optical microscopy lead to underestimates from 3% to 14% for case (iii) and up to 50% for case (ii). To minimize these errors one should use a high magnification objective lens with reflection or transmitted light microscopy, or electron microscopy.