Vanadium–titanium-bearing direct reduced iron (V-Ti DRI) is a promising feedstock for the full-value utilization of V-Ti magnetite. Selective partition of V and Cr into the metal phase, with Ti retained in the slag, requires quantitative thermodynamic guidance. We investigate this slag–metal distribution using the ion and molecule coexistence theory (IMCT). An eight-component slag model with 33 complex-molecule equilibria is coupled to reduction thermodynamics through an iterative mass-balance procedure; the metal-phaseWagner activity is temperature-scaled by Chipman’s rule, and the dissolved oxygen concentration is closed through the C-CO-O equilibrium. The equilibrium V and Cr recovery ceilings (metal side) rise from 89%/96% at 1400 °C to approximately 99.4% at 1500 °C and exceed 99.8% at 1550 °C. Ti-in-slag retention (slag side) drops steadily from 99.998% at 1400 °C to 99.4% at 1700 °C, giving a V/Ti separation factor above 104. Fe recovery to the metal phase exceeds 97% at 1600 °C and above, driven by the strong reduction of FeO, which constitutes approximately 32 wt.% of the initial slag. Carbon activity exerts a cubic power-law effect: at 1450 °C, the V recovery ceiling collapses from 97.4% at a_C = 1 to 6.5% at a_C = 0.05, identifying imperfect carbon saturation as a primary thermodynamic mechanism behind the ceiling-to-pilot gap. Once temperature and oxygen closure are enforced, the ceilings are only weakly sensitive to metallization, basicity, coke ratio, and TiO₂ content. Comparison with pilot data shows the ceilings exceed reported yields by 16–29 percentage points (pp), quantifying the kinetic/mass-transfer deficit and providing a benchmark for scale-up.

Sulfate roasting is a critical pyrometallurgical pre-treatment for extracting Cu and Co from low-grade Cu–Co–Fe sulfide ores, yet conventional phase diagrams provide limited quantitative guidance for process control. To address this gap, a multicomponent/multiphase thermodynamic equilibrium model based on Gibbs free energy minimization was developed to systematically investigate the oxidative roasting behavior of single sulfides (Cu₂S, CoS₂, FeS₂) and their ternary mixture, with respect to air supply, temperature, and total pressure. The model reveals that each sulfide follows distinct, temperature-dependent phase transformation pathways: Cu₂S forms the acid-leachable product CuO·CuSO₄ at temperatures ≤ 588 °C with a stoichiometric air supply of 11.9 mol, transitioning to oxides at ≥800 °C; CoS₂ converts completely to CoSO₄ below 727 °C and to CoO at higher temperatures; FeS₂ yields sulfate phases at low temperatures and iron oxides above 654 °C. In the ternary Cu₂S–CoS₂–FeS₂ system, competitive oxidation reactions produce refractory mixed oxides (CuO·Fe₂O₃, CoO·Fe₂O₃) whose formation is governed by temperature, air supply, and sulfide molar ratios. The results demonstrate that low-temperature roasting (≤641 °C) with precisely controlled air supply maximizes the formation of water-soluble sulfates, providing a quantitative thermodynamic basis for process optimization and enhanced recovery of Cu and Co from complex sulfide ores.

Effective iron removal from highly acidic leachates without neutralizer addition is a long-standing challenge in hydrometallurgy. For Cu-Co-bearing pyrite cinder, we demonstrate that a cyclic leaching process achieves this outcome. Operating entirely without neutralizers, the process consumed 96% of residual acid, enriched Cu and Co 4.76- and 3.88-fold, and removed 48.2% of iron, all while maintaining pH below 1.5 across four closed-loop cycles. Thermodynamic analysis reveals that Fe³⁺-${\mathrm{SO}}_4^{2-}$ complexation suppresses free Fe³⁺ to approximately 10⁻⁸ mol/L, ruling out conventional hydrolytic precipitation and directing precipitation towards schwertmannite-type basic ferric sulfate (Fe₈O₈(OH)₆SO₄). The formation of this sulfate-bearing Fe precipitate is consistent with the thermodynamic analysis, the iron mass balance, and a 176% increase in solid-phase sulfur. This neutralizer-free strategy offers a sustainable paradigm for recovering critical metals from iron-rich secondary resources.