Development and application of matte/speiss/metal thermodynamic database for optimization of processing of drosses, dusts and reverts from lead, zinc and copper production

Detrimental elements such as arsenic and antimony tend to accumulate in dusts and drosses of lead-zinc as well as copper smelters. These by-products are commonly treated in dedicated reductive smelting units producing Cu-rich matte, As-Sb-collecting speiss and Pb-rich metal, as well as liquid slag. Such process would have a complex distribution of elements (Cu, Fe, Pb, Zn, Ni, Sn, Sb, As, Ag, Au, S, etc.) among four liquid phases. Thermodynamic calculations can be used for predictions and optimization of such processes. They must rely on accurate models developed in integration with experimental program. Present study reports results of recent progress in experimental and modelling studies of As, Sb-containing speiss systems and demonstration of calculations relevant for industrial conditions. Experimental methodology consisted of equilibration, quenching and electron probe X-ray microanalysis. Calculations were performed using FactSage software and thermodynamic database developed based on the dedicated recent experiments. The main findings of the paper are: a set of binary and ternary diagrams relevant to matte and speiss formation conditions; distribution of Ag and Au among liquid Pb and speiss in key quaternary systems; and distributions of 10 main elements for industrially relevant matte/speiss/metal multicomponent equilibria.


Introduction
Modern lead and zinc pyrometallurgical production sites need to adapt to multiple, often conflicting, trends.All countries worldwide implement stricter environmental regulations.In Europe, Australia, and the USA, the perception of production sites as "polluting" has led to public pressure on both industries and governments.Production in these countries stagnated, and no major investment in metallurgical infrastructure was observed in 2010-2020 [1,2].In 2022, energy crisis in Europe lead to several shutdowns.As a consequence, metallurgical research and education in these countries have been underfunded, leading to reduced number of students [3].At the same time, the global shift towards renewable energy, if taken seriously, would require a substantial increase in base metal production, including lead and zinc [4].Hence, lower quality ores containing higher amounts of impurities such as arsenic and antimony would need to be incorporated into the production streams, posing challenges to traditional lead, zinc and copper processes.The signs of de-globalization have prompted governments to compile lists of critical metals or minerals.These lists are intended to secure manufacturing capability and often include antimony, bismuth, zinc, nickel, indium, and others, but not lead or copper [5].Metallurgy experts recognize that the recovery of "critical" elements from primary and secondary sources would heavily rely on lead, zinc, and copper pyrometallurgical infrastructure [6].However, accepting this fact requires a fundamental shift in the mindset of policymakers.
Several solutions addressing these challenges have been proposed.First, an expansion of end-user product recycling into primary metals production, often referred to as closing the gap in the circular economy [6].Second, a closer integration among lead, zinc, and copper primary and recycling processes with an exchange of "waste streams" [7].If implemented, this approach will enhance the recovery of all valuable metals and reduce the environmental impact of their disposal.The concept of such polymetallic integrated plant is shown in Figure 1 and was largely inspired by Alvear et al. [8], who recently reviewed existing polymetallic plants.The challenges of logistics and transport costs are evident, but they do not appear insurmountable, considering that nowadays many concentrates with relatively low contents of valuable metals travel thousands of kilometers from miners to smelters.Economics of the process can be evaluated and optimized using digital twins of metallurgical infrastructure [9].As shown in Figure 1, the combination of process units, smelting and separating the intermediate products among the slag, matte, speiss, metal phases would play an important role in integrated polymetallic plant.The "Zn-, Pb-dust" stream from gas cleaning systems would inevitably contain high concentrations of arsenic and copper [10].These must be removed from the main "Pb bullion" stream.The "Cu-Ni-dross" can be rich in Sb, Sn and S. Elements of slag/metal, matte/metal or speiss/metal separation exists in many lead smelters, and the chemistry is expected to grow more and more complex in future.The final flowsheet can only be developed by process engineers on-site because the compositions of streams are highly confidential.
The role of PYROSEARCH group is to provide fundamental information on high temperature chemistry, which is being used by the sponsor companies to simulate the individual process units.The research is based on integrated experimental and thermodynamic modeling studies.As a product, we provide computational tools capable of predicting the conditions of formation of phases, the distribution of all elements among these phases, and energy balance for the process.The present study reports some recent modeling and experimental results limited to the chemistry within the Cu-Fe-Pb-Zn-Ni-Sn-Sb-As-Ag-Au-S system.

Development of the thermodynamic database
Thermodynamic calculations of the present study are based on Gibbs energy minimization routine included in FactSage software [11].FactSage software also contains programmed mathematical expressions for the Gibbs energies of complex solution phases.These expressions in the form of G = f(T, P, x1..xn) are often referred to as thermodynamic models.In thermodynamic models, T is temperature, P is total pressure, and x1…xn are compositional variables.FactSage software was tested to perform reasonably fast and reliable calculations for 20 elements, dozens of potential phases, and thousands of bond fractions within the solution phases.Thermodynamic models contain adjustable parameters, which must be found from experiments, or in rare cases, from the first-principal methods, i.e. statistical thermodynamics or quantum mechanics.Examples of model parameters are enthalpy of formation, entropy, and heat capacity expressions (ΔHf°, S°, CP) for solution components, as well as energy parameters for the interactions between solution components.Thermodynamic models for possible phases together with a set of model parameters form a thermodynamic database.A portion of the database used in the present study is shown schematically in Table 1.
The modeling methodology used in the present study is based on CALPHAD principles.They can be formulated as follows: for a given chemical system (a group of elements), the thermodynamic database should contain a single set of model parameters for all potentially stable phases within the system.The combination of models and parameters should provide the best description different types of available experimental data, including information on phase equilibria, activity measurements, the distribution of elements among phases, calorimetry, and crystallography.In PYROSEARCH, these principles have been further expanded to proactively integrate thermodynamic modelling with experiments.In cases when experimental data are not available or contradictory, target experimental series are designed to fix certain model parameters.The results of these experiments are then included in the overall dataset and used to optimize all model parameters simultaneously.To determine the conditions of experiments, thermodynamic calculations with intermediate version of the database are used, which substitutes the trial-and-error approach.Still, the combinatorial nature of interactions among elements means that the number of sub-systems to be investigated using the CALPHAD approach is huge.For instance, the 11-composnent system from Table 1 requires complete thermodynamic assessment of 11!/2!/(11-2)!= 55 binary subsystems and 11!/3!/(11-3)!= 165 ternary subsystems.The number of quaternary and higher order systems is even higher, but they may be prioritized.The models in the present study only use binary and ternary interaction parameters, which reflect the physics of interactions on atomic level.Still, multicomponent experiments are necessary to verify and improve binary and ternary parameters.The following sections contain examples of thermodynamic modelling and experimental results.
The Modified Quasichemical Model (MQM) [12][13][14][15] used in the present study, a collaborative effort between CRCT (Montreal, Canada) and GTT (Germany).It has demonstrated its ability to describe the thermodynamics of many chemical systems, binary, ternary and of more components.Over the years, the model has undergone several improvements, as detailed in recent publications [16].These enhancements now offer greater flexibility in choosing constituents, formulating expressions for excess Gibbs energy, and interpolating binary parameters into ternary and higher-order systems.Notably, other established models, such as the Bragg-Williams ideal solution and the associate solution model can be reproduced within the MQM framework.Notable, the MQM was used not only for the liquid phase, but also for a number of solid solutions, as shown in Table 1.

Phase diagrams of key binary systems
Literature search has been conducted for all the binary sub-systems within Table 1.The available experimental results or thermodynamic assessments have been analyzed and used to establish model parameters.Examples of publications describing the optimization of model parameters are available for some systems: Pb-S [17], As-S [18], Cu-As [19], Pb-As [20].A summary of binary systems important for the matte formation is given in Figure 2 and Figure 3.The term "matte" is typically used for the molten sulfide-based material.In Figure 1, liquid matte is an important product in "Cu smelter" and "Cu converter" units.Copper is a "chalcogenic" element, which means it has strong interaction with sulfur.When a significant amount of copper enters lead production stream, it is separated in a form of liquid matte [21] or solid copper sulfides.In Figure 1, the formation of liquid matte is expected in "Pb blast furnace", but separation will be conducted in continuous or batch-type "Drossing" units.As can be seen in Figure 2, there a is miscibility gap between metal and sulfide liquids in the Cu-S system.Iron, nickel and lead do not form a miscibility gap with sulfide, which means metal and matte phases generally must be described using a single liquid solution thermodynamic model.Other elements, such as tin, antimony, or silver do form miscibility gaps with sulfides (Figure 3).Arsenic and zinc are very volatile.The metallic phases in the As-S and Zn-S systems can only be observed if high external pressure is applied.Solid zinc sulfide has a remarkably high melting point.
Figure 4, Figure 5 and Figure 6 show important binary systems to understand the "speiss" phases.Speiss can be defined as a series of solid compounds and liquids that are formed due to the strong interaction between d-metals (Fe, Co, Cu, Ni, Zn) and metalloids (As, Sb) [22].Tin (Sn) is sometimes also included as speiss-forming component because of high-melting solid phases with Cu, and particularly with Ni.No liquid miscibility gaps are observed, except for the Fe-Sn system.Metallic lead does not form high melting phases or miscibility gaps with As, Sb or Sn (Figure 6).Thus, from the modelling point of view, liquid metal and liquid speiss again must be described as a single solution.Historically, the word speiss was first used in Germany to characterize some of the products of the "drossing" process of lead bullion.These phases mainly consist of Cu-As, Cu-Sb, Fe-As, Ni-As, or Ni-Sb compounds [23].The formation of a solid speiss crust on top of molten lead is a key step in lead fire refining after first copper drossing, but it also may negatively interfere with the separation of copper in a form of liquid matte [24].Typically, solid speiss compounds are considered as undesirable by-products and very few companies are willing to treat them to extract metals.Other areas of potential speiss formation in Figure 1 are: Fe-As and Zn-As compounds in the products of corrosion of steel jackets in the "Pb blast furnace" [25], droplets of Cu-As, Cu-Sb, and Fe-As in the slag of "Zn fuming [26].

Phase diagrams of key ternary systems
The liquid-liquid equilibria important for the matte/metal or speiss/metal is summarized in Figure 7.There is a good separation between lead-based metal and matte, but the separation between lead-based metal and speiss exists only under certain conditions: the Cu/As, Cu/Sb or Cu/Sn ratio show be high enough to result in the appearance of the miscibility gap.The extension of the miscibility gap in the Pb-Cu-As, Pb-Cu-Sb and Pb-Cu-Sn is the topic of current experimental research.Earlier publications [27,28] showed very wide gap at 1200 °C, both for Pb-Cu-As and Pb-Cu-Sb systems, which is now believed to be incorrect, as explained in the paper by the authors [20].It is believed that no liquid-liquid miscibility exists at 1200 °C in the Pb-Cu-As system, but it does exist at lower temperatures, i.e. 900 °C.

Example of quaternary system experiments and modelling
The partitioning of precious metals, such Ag and Au in solid or liquid speiss an important factor and can motivate companies to further process them before dumping.Thus, it is important to know the distribution of Ag and Au for liquid-liquid equilibria involving speiss [29].Some works are available for distribution of precious metals between lead and iron-rich speiss [30], between matte and iron-rich speiss [31], and between matte and copper-rich speiss [32], but no study was found for the distribution between lead and Cu-rich speiss.A series of 20 experiments was designed to verify and improve the thermodynamic model.The experimental methodology involved high temperature equilibration of experimental mixtures at controlled conditions, rapid cooling (quenching) of the samples and direct measurement of the compositions of equilibrium phases using Electron Probe X-ray Microanalysis (EPMA) [22].Figure 8 and Figure 9 show a typical microstructure, schematic location of liquid-liquid two phase zone inside the tetrahedron and compositions of obtained phases.The black tie-line inside the tetrahedron approximately shows the compositions targeted in the experiment.The perfect quenching and polishing are very hard to achieve for these types of systems, but significant progress has been achieved for these extremely fluid liquids over the last years, and the results are believed to have the necessary statistical significance to verify and improve the thermodynamic database.The results of this experimental series, together with available literature data were used to improve the description of the Cu-Ag-As, Cu-Au-As, Cu-Ag-Sb, Cu-Au-Sb, Cu-Ag-Sn ternary sub-systems.The concentrations of Ag and Au in the experiment were quite high.Blue symbols represent experimental results and red symbols are model predictions for the same bulk composition as in experiment.Good agreement was achieved, which provides the confidence of model predictions at lower concentrations of Ag and Au.

Experiments and modelling for industrially relevant multicomponent equilibria
Several companies-sponsors of PYROSEARCH were interested in the potential for the conditions of 3liquids matte/speiss/metal equilibrium which may be realized during the lead reduction process with high input of secondary complex materials.A series of 10 multicomponent experiments has been designed.Figure 11 shows some of the results for this type of equilibria.Due to very low viscosities of liquids, it is virtually impossible to achieve the perfect quenching, but valuable information can be obtained.The overall idea of the measurement is that droplets observed within the phase regions appeared during the quenching and must be included in the measurement by averaging many points over the regions and using relatively large diameter of electron beam in EMPA.The assumption is that no cross contamination existed outside of the established phase regions at the temperature of equilibrations, and that the quenching rate was sufficiently fast to prevent further segregation and growth of phase regions.By itself, these assumptions seem too big, but the accumulated experience in micrographs of hundreds of tests gives certain confidence.Model calculations also allow to cross-check challenging experiments with simpler and well-established experiments.
Different microstructures were obtained for the sample with the same bulk compositions at 1100 and 1000 °C, indicating the transition from 2-liquids to 3-liquids equilibria.Thermodynamic calculations were performed using FactSage software with the J-option on Liquid matte/metal/speiss solutions, allowing 3-phase immiscibility.Essentially, it adds 3 copies of the same multicomponent solution, which is substantially more complicated than a typical equilibrium calculation.The model reproduces the appearance of additional metal/speiss immiscibility between 1100 and 1000 °C, after small corrections were made within earlier model for the Cu-Pb-As system [20].These corrections were supported by unpublished experimental results within the Cu-Pb-As system.The calculated miscibility gap between metal and matte is somewhat "wider" compared to the experiment, which is mainly observed as lower concentration of Cu, Fe and S in the lead bullion (metal phase), and higher calculated mass of matte for a given virtual bulk composition.The detailed analysis of the distribution of all other elements is outside of the scope of this publication.Overall, 10 multicomponent experiments (Figure 10) have been done, and the difference between the model predictions and measured compositions is shown in Figure 11 and Figure 12.
The challenge of establishing the correct solubility of Cu and S in metallic lead in the range of temperatures between 1000 and 1200 °C for the Cu-Pb-S system have been discussed in 2020 publication [17].Since then, more data have been produced, resulting in a decision an increase the solubility compared to the model of 2020 [17].The results in Figure 11 suggest even further increase of solubilities within the Pb-Fe-Cu-S system, which now cannot be reproduced by the model without compromising the data in ternary-subsystems.An argument can be made that some of the droplets observed in metal region were entrained at the temperature of equilibration and did not appear during the quenching.Let's assume the model indeed overestimates the amount of mass produced, compared to reality, and it is used in industrial for the simulation of the process unit.In this case, several kinetic factors would have to be introduced.Suspension indices, reflecting imperfect settling of droplets compared to equilibrium would mask some of model imperfection.If we assume that the model is correct, the suspension indices would still be required and calibrated based on the operation of the specific unit.Thus, the model provides reasonable approximation, which in any case requires correction.

Conclusions
The fundamentals of the matte/speiss/metal equilibria, which are important for the increasing integration among Pb, Cu and Zn processes have been reviewed.Present study provides the set of assessed binary and ternary diagrams which can be used to understand the conditions of metal/matte/speiss formation.Also, the distribution of Ag and Au among liquid Pb and speiss in key quaternary systems, Pb-Cu-As-Ag, Pb-Cu-As-Au, Pb-Cu-Sb-Ag, Pb-Cu-Sb-Au and Pb-Cu-Sn-Ag, have been measured and compared with model predictions.The distributions of Pb, Cu, Ni, As, Sb, Sn, Fe, S, Zn and Ag among matte, speiss and metal have been measured for conditions, relevant to recycling of WEEE using the reductive smelting of Pb route.The model reasonably describes these challenging experiments.

Figure 1 .
Figure 1.The concept of future integrated polymetallic plant.Flowsheet configuration separating slag/matte/speiss/metal in the center is to be determined in future.

Figure 2 .
Figure 2. Phase diagrams of matte forming binary systems at 1 atm total pressure: Fe-S, Ni-S, Cu-S, Zn-S.Lines are calculated using thermodynamic database of the present study based on assessment of experimental data.

Figure 3 .
Figure 3. Phase diagrams of matte forming binary systems at 1 atm total pressure: Pb-S, Sn-S, Ag-S, As-S and Sb-S.Lines are calculated using thermodynamic database of the present study based on assessment of experimental data.

Figure 4 .
Figure 4. Phase diagrams of speiss forming binary systems at 1 atm total pressure: Fe-As, Fe-Sb, Fe-Sn, Ni-As, Ni-Sb, Ni-Sb.Lines are calculated using thermodynamic database of the present study based on assessment of experimental data.

Figure 5 .
Figure 5. Phase diagrams of speiss forming binary systems at 1 atm total pressure: Cu-As, Cu-Sb, Cu-Sn, Zn-As, Zn-Sb, Zn-Sb.Lines are calculated using thermodynamic database of the present study based on assessment of experimental data.

Figure 6 .
Figure 6.Phase diagrams of speiss forming binary systems at 1 atm total pressure: Pb-As, Pb-Sb, Pb-Sn.Lines are calculated using thermodynamic database of the present study based on assessment of experimental data.

Figure 7 .
Figure 7. Phase diagrams showing matte/metal and speiss/metal immiscibility: Pb-Cu-S, Pb-Fe-S, Cu-Fe-S, Pb-Cu-As, Pb-Cu-Sb and Pb-Cu-Sn.Lines are calculated using thermodynamic database of the present study based on assessment of experimental data.

Figure 8 .
Figure 8. Example micrograph and schematic location of tie-line for the series of 20 experiments for the distribution of elements in the Pb-Cu-As-Ag, Pb-Cu-As-Au, Pb-Cu-Sb-Ag, Pb-Cu-Sb-Au and Pb-Cu-Sn-Ag systems.

Figure 9 .
Figure 9.A series of 20 experiments for the distribution of elements in the Pb-Cu-As-Ag, Pb-Cu-As-Au, Pb-Cu-Sb-Ag, Pb-Cu-Sb-Au and Pb-Cu-Sn-Ag systems.Blue symbols are measured compositions, red symbols are model predictions using thermodynamic database of the present study.

Figure 12 .
Figure 12.Root mean square difference in the compositions of matte, bullion and speiss between the experiment and model for 10 equilibrium experiments.

Table 1 .
A portion of thermodynamic database used in the present study for the calculations within the Cu-Fe-Pb-Zn-Ni-Sn-Sb-As-Ag-Au-S system.Cu II , Fe II , Fe III , Pb II , Zn II , Ni II , Sn II , Sb III , As III , Ag I , Au I , S II )