The phase equilibria of the ZnO-"FeO 1..5 ", ZnO-"FeO 1.5 "-SiO 2 , PbO–ZnO-"FeO 1.5 " and PbO–ZnO-"FeO 1.5 "-SiO 2 slag systems in equilibrium with air or metallic lead/iron were studied as part of the investigation of the 19-component PbO–ZnO–Cu 2 O–FeO–Fe 2 O 3 –CaO–SiO 2 –Al 2 O 3 –MgO–S-(As, Sn, Sb, Bi, Ag, Au, Ni, Cr, Co as minor elements) slag/matte/metal/speiss/gas system, supporting the operation/development of existing and emerging pyrometallurgical processes. In the experimental part of the study, samples underwent high temperature equilibration followed by quenching, and the direct measurement of the lead, zinc, iron and silicon concentrations in the liquid slag, solid oxide, and metal phases by electron probe microanalysis (EPMA). The a) massicot (PbO), b) spinel ((Zn, Fe)Fe 2 O 4), c) zincite ((Zn,Fe)O 1+x , 2 polymorphs), d) lead ferrite (Pb 2+x Fe 2 O 5+x), e) plumboferrite (Pb 4 Fe 22-x Zn x O 37), f) magnetoplumbite (Pb(Fe 2 O 3 ,PbFeO 2 ,PbZnO 2)Fe 10 O 16), and g) W-ferrite (PbZn 2-x Fe 16+x O 27) primary phase fields of the PbO–ZnO-"FeO 1.5 " system in equilibrium with air were studied between 780 and 1300 °C. The ZnO-"FeO 1.5 ", ZnO-"FeO 1.5 "-SiO 2 and PbO–ZnO-"FeO 1.5 "-SiO 2 systems in equilibrium with air were studied up to 1745 °C, significantly improving the availability of information on the composition range of the high- and low-Fe zincite ((Zn,Fe)O 1+x) phases, and on the liquid slag composition at the boundaries of their primary phase fields. Lastly, the solubilities of iron in larsenite (Pb(Zn,Fe)SiO 4) and melilite (Pb 2 (Zn,Fe)Si 2 O 7) in equilibrium with air or metal were studied between 700 and 800 °C. The newly obtained and existing experimental data were used to develop a self-consistent set of thermodynamic parameters describing all phases in the system using the FactSage computer package. [ABSTRACT FROM AUTHOR]