Mass-metallicity diagram showing the occurrence of PIEs during the early AGB phase. The corresponding [Fe/H] ratios are indicated on the right axis assuming solar-scaled mixtures. Red filled circles show AGB models experiencing a PIE when f_top = 0. Empty black circles are for models that do not experience a PIE when f_top = 0. Thick black circles denotes models computed in this work and in Paper III. The small red circles and red dots highlight our models that experience a PIE when f_top = 0.04 and 0.10, respectively. The other models are from Iwamoto et al. (2004), Campbell & Lattanzio (2008), Cristallo et al. (2009a, 2016), Lau et al. (2009), Suda & Fujimoto (2010). The four colored zones show the approximate PIE zone when f_top = 0, 0.02, 0.04 and 0.10.