Kinetics of solid-state oxidation of iron, copper and zinc sulfide mixture published by Ural Federal University eISSN 2411-1414 chimicatechnoacta.ru ARTICLE 2023, vol. 10(2), No. 202310202 DOI: 10.15826/chimtech.2023.10.2.02 1 of 12 Kinetics of solid-state oxidation of iron, copper and zinc sulfide mixture Alexander M. Klyushnikov , Sergey M. Pikalov , Roza I. Gulyaeva * Laboratory of Non-Ferrous Metals Pyrometallurgy, Department of Non-Ferrous Metals, Institute of Metallurgy of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg 620016, Russia * Corresponding author: amk8@mail.ru This paper belongs to a Regular Issue. Abstract The kinetics of solid-state oxidation by air of iron, copper and zinc sulfide natural mixture, which is typical of the pyritic copper ores, is investigated. Using the high-temperature X-ray powder diffraction, thermogravimetry and differential scanning calorimetry, it was found that the process can be represented by five exothermic elementary reactions, corresponding to in- tensive burning of iron, copper and zinc sulfides, and two endothermic ones, associated with decomposition of copper and iron sulfates. Kinetic analysis is performed by Kissinger and Augis–Bennett methods, the model-free func- tion mechanism was determined from y(α) master plots and iterative opti- mization of the kinetic parameters. The limiting steps of these reactions are nucleation and crystal growth, and the values of activation energy, pre-expo- nential factor and Avrami exponent are in the ranges of 140–459 kJ·mol–1, 1.41·104–3.49·1031 s–1, and 1.0–1.7, respectively. Crystallization is followed by an increase in the number of nuclei, which may be formed both at the interface and in the bulk of the ore particles, and crystal growth is one-di- mensional and controlled by a chemical reaction at the phase boundary or diffusion. The results of the work can contribute to the development of the- oretical ideas about the physicochemical transformations of pyritic ores and concentrates during pyrometallurgical operations. Keywords iron sulfide copper sulfide zinc sulfide pyritic copper ore oxidation kinetics Received: 16.03.23 Revised: 18.03.23 Accepted: 20.03.23 Available online: 30.03.23 Key findings ● The formal kinetics of the sulfides, oxidation is attributed to seven elementary reactions. ● The activation energy of the elementary reactions is 140–459 kJ·mol–1. ● The limiting steps of the elementary reactions are nucleation and crystal growth. ● Nuclei may be formed both at the interface and in the volume of the ore particles. ● Crystal growth is one-dimensional and is controlled by a chemical reaction or diffusion. © 2023, the Authors. This article is published in open access under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). 1. Introduction Currently, pyritic copper ores are primarily processed ac- cording to the scheme that includes the following opera- tions: comminuting and froth flotation of initial ore with the separation of sulfide concentrate, autogenous matte smelting of the concentrate, converting of the matte into blister copper, and fire refining and electrorefining of the blister copper to cathode copper. The matte smelting and converting slags are depleted by flotation, the resulting concentrates are returned to matte smelting, and the depleted slag is sent to the dump. The off-gases from matte smelting and converting are utilized in the production of sulfuric acid. The final products of the technology are cath- ode copper, slags, sulfuric acid, and electrolytic slime that concentrates precious and rare metals [1]. Massive and disseminated ores of pyritic copper depos- its from the Urals region (Russia) may have an increased (up to 0.2 mass%) content of cobalt [2, 3], and there is a need for its associated extraction in commercial products. The cobalt output channel in the scheme described above is the converter slag; smelting with a carbonaceous reducing http://chimicatechnoacta.ru/ https://doi.org/10.15826/chimtech.2023.10.2.02 http://creativecommons.org/licenses/by/4.0/ https://orcid.org/0000-0001-8239-3757 https://orcid.org/0000-0001-6292-0468 https://orcid.org/0000-0003-2860-0377 https://crossmark.crossref.org/dialog/?doi=https://doi.org/10.15826/chimtech.2023.10.2.02&domain=pdf&date_stamp=2023-03-30 Chimica Techno Acta 2023, vol. 10(2), No. 202310202 ARTICLE 2 of 12 DOI: 10.15826/chimtech.2023.10.2.02 agent and a sulfidizer (sulfide concentrate) can be used to extract a cobalt-rich sulfide product suitable for processing by conventional methods. The problem is that the fine in- tergrowth of ore minerals and high solubility of non-fer- rous metals in pyrite are the reasons of transition of up to 95% of cobalt into the waste products during flotation of the ores [4]. Processing the entire mass of the ore according to the described scheme is limited for technological and economic reasons. A promising route for the processing of pyritic copper ores from the Urals can be their direct partial oxidative roasting in a fluidized bed furnace at 800–900 °C with the transfer of up to 80% of sulfur into the gas phase (in this case, a significant part of the calorific capacity of the ore will be used) and the use of the resulting calcine as a sul- fidizing agent in the reduction-sulfiding smelting of oxi- dized nickel-cobalt ores (laterites) from the deposits of the same region, which are not currently processed [5]. Varying the proportions of the roasted pyrite ore and oxidized nickel-cobalt ore in the feed of matte smelting will allow: i) regulating the yields and compositions of the smelting products; ii) controlling sulfur distribution, where most of the sulfur in the form of SO2-rich roasting gases will be di- rected to manufacturing sulfuric acid, and the remainder will be spent for nickel and cobalt sulfiding of oxidized nickel ore during matte smelting; iii) extracting nickel, cop- per, cobalt and precious metals into the matte containing up to 10 mass% Ni+Cu+Co (at the same time, the presence of copper in the matte will reduce the loss of nickel and co- balt in slag [6]); iv) eliminating or minimizing the need for fluxes by using the fluxing potential of the ores; v) obtain- ing the final slag in the final step of the scheme [7, 8]. We have conducted research towards the development of the scientific basis and the feasibility study of this method [9– 13]. An important aspect of the technology is the intensity of oxidative roasting of the copper ore, which determines the specific productivity of the fluidized bed furnace and temperature and duration of the process; for its evaluation, information on the chemistry, kinetics, and mechanism of roasting is needed. A lot of publications are devoted to these questions in relation to copper-nickel ores [14], copper [15– 27], zinc [17, 28, 29], nickel [30, 31], and copper-cobalt [32] concentrates, as well as individual sulfide minerals which are part of them: pyrite [33–46], marcasite [47], macki- nawite [48], pyrrhotite [34, 36, 39, 49–54], chalcopyrite [36, 47, 55–59], covellite [60], chalcocite [47, 60–62], zinc sulfide [63–69], cobalt sulfide [70], and their mixtures [71, 72]. The purpose of the present work is to study the kinetics and mechanism of solid-state oxidation of iron, copper and zinc sulfide natural mixture, typical of the pyritic copper ores. 2. Experimental For the study, a representative sample of a pyritic copper ore from the Dergamysh deposit (Russia) was taken; the sample was ground in a laboratory mill to a particle size of less than 0.1 mm. The chemical composition of the ore sample was inves- tigated by inductively coupled plasma atomic emission spectrometry (ICP AES) on an iCAP 6300 Duo optical emis- sion spectrometer (Thermo Scientific). Preparations for analysis were carried out by dissolving a sample weighing 0.1 g in a mixture of mineral acids. The thermal properties of the ore sample were studied by the method of simultaneous thermogravimetry (TG) and differential scanning calorimetry (DSC) on a STA 449 C Ju- piter® instrument for synchronous thermal analysis (NETZSCH). For measurements, about 8.4 mg of the sample was distributed in a thin layer at the bottom of a corundum crucible, after which the crucible was placed into the meas- urement cell of the instrument and heated from 30 to 1100 °C at a rate of βi = 5, 10, and 20 °C·min–1 (hereinafter, the subscript "i" denotes the i-th temperature program (i = 1, 2, 3)). Dynamic oxidizing atmosphere in the reaction space was maintained by blowing the measurement cell with dried synthetic air (21 vol% O2, 79 vol% N2) supplied at a flow rate of 30 cm3·min–1. The empty reference crucible was the same as the sample crucible. The DSC correction parameters were estimated from the enthalpy of fusion of chemically pure (99.99 mass%) indium using the NETZSCH Thermokinetics 3.0 software. The composition of gases evolved during heating was evaluated by mass spectrome- try (MS), for which a quadrupole QMS 403 C Aёolos® mass spectrometer (NETZSCH) was coupled with the thermal analyzer; ionic current (I, A) of gases (H2O, CO2, SO2, and SO3) released during heating and oxi- dation of the ore was measured in the mode of given mass numbers. The processing of the measurement results was made using the NETZSCH Proteus® 5.1 software, including the identification of the onset (To, °C), maximum (Tp, °C), and endset (Te, °C) temperatures, and areas (ΔH, J·g–1) for DSC peaks, relative mass changes (Δm, %), and peak tem- peratures (TpH2O, TpCO2, TpSO2, and TpSO3, °C) of the ionic cur- rent curves of H2O, CO2, SO2, and SO3. Separation of com- plex DSC peaks into their constituent overlapping elemen- tary peaks and determination of their onset (Toij, °C), max- imum (Tpij, °C), and endset (Teij, °C) temperatures, as well as the values of their full width at the half of maximum (ΔTpij, °C) were performed using the MathWorks software according to the method outlined in [73]. The baseline was characterized by a linear function, and the profile of ele- mentary peaks was approximated by Frazer–Suzuki (asym- metric Gaussian) function. For each temperature, the value of the function describing the complex peak was elaborated as the sum of such values for elementary peaks, and the re- liability of approximation (for significance level α = 5%) was controlled by the value of Pearson correlation coeffi- cient (r). The measurement error was ±0.01 mg for mass, ±3 °C for temperature, and ±5% for heat. The phase composition of the ore sample was deter- mined by X-ray powder diffraction (XRD) on DRON-2.0 X- https://doi.org/10.15826/chimtech.2023.10.2.02 https://doi.org/10.15826/chimtech.2023.10.2.02 Chimica Techno Acta 2023, vol. 10(2), No. 202310202 ARTICLE 3 of 12 DOI: 10.15826/chimtech.2023.10.2.02 ray diffractometer. Experiments on oxidative roasting of the ore combined with evaluation of the phase composition of the products using high-temperature XRD (HTXRD) method were performed in the high-temperature UVD– 2000 setup mounted on the above device, equipped with a resistance furnace with a platinum heating element; the de- sign of the setup provided free atmospheric air access to the working chamber. The experiment included heating the in- itial ore at an average rate of 10 °C·min–1 from 25 °C to a given temperature (100, 200, 300, 400, 500, 600, 700, 800, and 900 °C) and isothermal dwelling at this tempera- ture for 80 min. At the same time, as mentioned above, in situ diffractograms were recorded in the isothermal sec- tions of the cycles. The measurements were conducted in the following mode: Bragg–Brentano geometry; Cu Kα radi- ation (λα = 1.54056 Å); graphite monochromator on the out- put beam; tube voltage and current of 30 kV and 30 mA, respectively; angular range (2θ) and step (2θ) of 10–90° and 0.02°, and point exposure time of 2 s at 25 °C and 1.2 s for high-temperature measurements. The samples for the experiment were prepared by applying 1–3 mg of a powdery (<0.1 mm particle size) material to a substrate made of plexiglas or (Zr,Y)O2–x. The temperature was measured with a type S thermocouple, the hot junction of which was placed near the sample (the measurement error was ±2 °C). Phase identification and semi-quantitative (with an error of ±5 relative %) estimation of the contents in the crystal component of the samples were performed by the reference intensity ratio (RIR) method [74, 75] using the QualX 2.0 software [76] and the Pow_Cod database [76]. Based on HTXRD data, a possible sequence of chemical reactions tak- ing place at the studied temperatures was established; the values of reaction equilibrium constants (KT) at tempera- ture T (K) were calculated using the HSC Chemistry 6.12 package (Outotec Research Oy). The microstructure and local elemental composition of the ore sample were studied by scanning electron micros- copy (SEM) and energy dispersive spectrometry (EDS) us- ing a MIRA 3 LMU auto emission electron microscope (TESCAN) equipped with an INCA Energy 350 X-max 80 en- ergy dispersive X-ray spectrometer (Oxford Instruments). SEM imaging was performed at an accelerating voltage of 20 kV, an electron beam current of 20 nA, and an effective beam resolution of 3 μm. During the preparation of the specimen for analysis, a sample was embedded into bake- lite, the surface of the cured cylindrical block was polished and coated with a thin carbon layer layer (25 nm). Kinetic analysis of the oxidation of the ore was per- formed by mathematical treating of DSC heating data of its sample for three temperature programs (βi = 5, 10, and 20 °C·min–1) in the boundaries of exothermic and endother- mic peaks corresponding to the development of this pro- cess. First, the inverse kinetic problem was solved, i.e., the kinetic parameters of oxidation were determined based on the experimental data. For this purpose, each j-th (j = 1, 2, …, N) elementary DSC peak was considered as a trace of the j-th formal irreversible one-step reaction Aj → Bj, where Aj and Bj are the initial formal reagent and the final formal product, respectively (both the complex and simple i-th curve peaks obtained by separation were counted as ele- mentary peaks). The completion and intensity of the j-th reaction at the i-th temperature program were quantified through conversion degree (αij) and reaction rate (dαij/dt, s–1) of Aj → Bj transformation [77, 78] according to the equations: α𝑖𝑗 = ∫ ( d𝐻𝑖𝑗 (𝑡) d𝑡 ) d𝑡 𝑡 𝑡0𝑖𝑗 ∫ ( d𝐻𝑖𝑗 (𝑡) d𝑡 ) 𝑡e𝑖𝑗 𝑡0𝑖𝑗 d𝑡 = ∫ ( d𝐻𝑖𝑗 (𝑇) d𝑇 ) d𝑇 𝑇 𝑇0𝑖𝑗 ∫ ( d𝐻𝑖𝑗 (𝑇) d𝑇 ) 𝑇e𝑖𝑗 𝑇0𝑖𝑗 d𝑇 , (1) dα𝑖𝑗 d𝑡 = 𝑘𝑗 (𝑇) 𝑓𝑗 (α𝑖𝑗 ) = 𝐴𝑗 exp (– 𝐸𝑗 𝑅𝑇 ) 𝑓𝑗 (α𝑖𝑗 ), (2) where toij and teij are the initial and final moments of the reaction (that is, the moments of the beginning and the end of the deviation of the DSC curve from the baseline), respec- tively, s (toij = 0 s); t is the current reaction time, s (toij < t < teij); Toij and Teij are the temperatures of the be- ginning and the end of the reaction, respectively, K; T is the temperature at the current time moments of the reaction, K (Toij < T < Teij); Hij(T) and Hij(t) are the functions describing the dependence of reaction enthalpy on temperature and time, respectively, J·g–1; kj(T) is the reaction rate constant invariant with respect to the temperature program, s–1; fj(αij) is the reaction model invariant with respect to the temperature program (i.e. a function reflecting the reaction mechanism); Ej is the effective activation energy invariant with respect to the temperature program, J·mol–1; Aj is a pre-exponential factor invariant with respect to the tem- perature program, s–1; R is the gas constant, J·mol–1·K–1. In the calculations it was assumed that the temperature changes over time according to a linear law: 𝑇 = 𝑇0𝑖𝑗 + β𝑖 𝑡, (3) and βi = dT/dt = Const. The Johnson–Mehl–Avrami– Erofeev–Kolmogorov (JMAEK) model [78, 79] was used as the reaction model fj(αij) (its choice is due to the reaction model identification results described below): 𝑓(α𝑖𝑗 ) = 𝑛𝑗 (1 – α𝑖𝑗 ) [– ln(1 – α𝑖𝑗 )] (𝑛𝑗 –1)/𝑛𝑗 , (4) which is based on the following equation describing the ki- netics of nucleation and crystal growth of the new phase in the parent phase α𝑖𝑗 = 1 – exp (– 𝑘𝑗 𝑡 𝑛𝑗 ) = 1 – exp [– 𝐴𝑗 exp (– 𝐸𝑗 𝑅𝑇 ) ( 𝑇−𝑇o𝑖𝑗 β𝑖 ) 𝑛𝑗 ]; (5) here nj is the Avrami exponent invariant with respect to the temperature program, which depends on the mechanism of the process. The initial estimation of the apparent activa- tion energy (Ej, J·mol–1) and the pre-exponential factor (Aj, s–1) was performed by the Kissinger method [78, 80]; the method is based on estimating the slope (–Ej/R) and https://doi.org/10.15826/chimtech.2023.10.2.02 https://doi.org/10.15826/chimtech.2023.10.2.02 Chimica Techno Acta 2023, vol. 10(2), No. 202310202 ARTICLE 4 of 12 DOI: 10.15826/chimtech.2023.10.2.02 intercept (ln(AjR/Ej)) of a pairwise linear regression for the model ln ( β𝑖 𝑇p𝑖𝑗 2 ) = ln 𝐴𝑗 𝑅 𝐸𝑗 − 𝐸𝑗 𝑅𝑇p𝑖𝑗 , (6) constructed from the pairs of observed values of ln(βi/Tpij2)–1/Tpij for each βi. The reliability of approxima- tion was controlled by the value of the coefficient of de- termination (Rj2). In order to identify the reaction model for the j-th reaction at the i-th temperature program, nu- merical values of the reference function yij(αij) were cal- culated for a given series of values αij varying from 0.1 to 1 in step of 0.1: 𝑦(α𝑖𝑗 ) = ( dα𝑖𝑗 d𝑡 ) α𝑖𝑗 exp ( 𝐸𝑗 𝑅𝑇α𝑖𝑗 ) ; (7) then the pairs of yij(αij)–αij for each βi were plotted on the coordinate plane and the resulting curves were compared with the theoretical plots of the function y(α) for the tabu- lated forms f(α). The reaction model selection was based on qualitative correspondence between the experimental and theoretical curves. The invariant Avrami exponent (nj) of the j-th reaction was determined by the Augis–Bennett method [81]; the cal- culation was performed using the formulae: 𝑛𝑗 = 1 3 ∑ 𝑛𝑖𝑗 3 𝑖=1 , (8) 𝑛𝑖𝑗 = 2,5𝑅𝑇p𝑖𝑗 2 𝐸𝑗 Δ𝑇𝑖𝑗 , (9) where nij is the Avrami exponent of the j-th reaction for the i-th heating rate; the value of Ej (J·mol–1) was taken from the Kissinger analysis. After that, the following iter- ations were performed: the values of invariant kinetic pa- rameters of elementary reactions (Ej, Aj, and nj) were sub- stituted into equation (5), analytical expressions were found to estimate the conversion degree (αij) for each j-th reaction and i-th temperature program, calculated kinetic curves αij–T were reconstructed, and, by varying the pa- rameter Aj from its initial value at fixed Ej and nj, the ob- tained model was optimized by approximating experi- mental curves with the calculated ones (the quality of ap- proximation at this and subsequent iterations was con- trolled by the value of the Pearson correlation coefficient (rij)). The refined value of the invariant pre-exponential factor (Arj, s–1) was obtained as the arithmetic mean of the optimal Aj values for all temperature programs. Then ob- tained Arj value was substituted into equation (5), the pa- rameters Arj and nj were fixed, and the model was opti- mized by varying Ej from its initial value to obtain a refined invariant value of the activation energy (Erj, J·mol–1). At the final stage of optimization, the fixed values of Erj and Arj were substituted into equation (5) and the model was op- timized by varying nj from its initial value to determine the refined invariant value of the Avrami exponent (nrj). The optimum invariant kinetic parameters found were used to solve a direct kinetic problem in relation to the ore oxidation process in the studied range of temperature pro- grams; by substituting Erj, Arj, and nrj values into equa- tions (5) and (2), analytical expressions were obtained to calculate the conversion degree (αj) and conversion rate (dαj/dt, s–1) at for the elementary reactions. Verification of the models for each reaction was carried out by as- sessing the closeness of the correlation between theoreti- cal and experimental data; for this purpose, refined calcu- lated kinetic curves αij–T were suggested and compared with the experimental ones; the Pearson correlation coef- ficient averaged over all temperature programs (ravj) served as the optimality criterion: 𝑟av𝑗 = 1 3 ∑ 𝑟𝑖𝑗 . 3 𝑖=1 (10) 3. Results and Discussion According to the ICP AES data, the original ore has the fol- lowing composition, mass%: 0.98 Cu, 0.01 Ni, 0.10 Co, 0.78 Zn, 38.5 Fe, 30.2 S, 0.03 As, 17.0 SiO2, 0.9 CaO, 6.7 MgO, and 4.8 others. At the ordinary content of copper (0.98 mass%) and zinc (0.78 mass%) it is characterized by higher (0.10 mass%) content of cobalt. The approxi- mate mass fractions of sulfides and rock-forming compo- nents are 63.3% and 36.7%, respectively. According to the XRD data (Figure 1) the total content of sulfide phases in the initial ore sample, determined by the RIR method, is 42.4 mass%; among the revealed minerals pyrite (FeS2), chalcopyrite (CuFeS2), and wurtzite (ZnS) can be noted, the fractions of which are 30.7, 3.1, and 8.6 mass%, re- spectively. There are barren minerals in the rest of the ore (57.6 mass%), such as: tremolite (Ca2Mg5H2(SiO3)8), si- derite (FeCO3), and quartz (SiO2), whose fractions are 17.1, 2.6, and 38.0 mass%, respectively. Figure 1 XRD patterns of the initial ore at 25 °C (the reflections of zirconium dioxide refer to the substrate). https://doi.org/10.15826/chimtech.2023.10.2.02 https://doi.org/10.15826/chimtech.2023.10.2.02 Chimica Techno Acta 2023, vol. 10(2), No. 202310202 ARTICLE 5 of 12 DOI: 10.15826/chimtech.2023.10.2.02 The SEM and EDS study showed that the ore has a full- crystalline porphyry-like fine-grained structure character- ized by close germination of sulfide and oxide phases, and has a massive (disordered) texture. In the matrix repre- sented by magnesium silicate, there are hydrated iron (III) oxide, and iron and calcium carbonates of the compositions Mg3Si4O10(OH)2 (talc), Fe2O3·nH2O (limonite), FeCO3 (sider- ite), and CaCO3 (calcite) respectively. In addition, there are distributed phenocrystals (5–150 μm) of iron sulfide corre- sponding in composition to pyrite (FeS2), and small (up to 5 μm) inclusions with sphalerite (Zn1–xFexS) and chalcopy- rite (CuFeS2) formulae. The data on the composition and structure of the ore ob- tained by XRD, SEM, and EDS methods complement each other and satisfactorily agree with the data obtained earlier for the ore of the same deposit [3, 4]. Summarizing the data obtained in the present work, we can conclude that the main ore minerals of the studied sample may be pyrite, pyr- rhotite, chalcopyrite, sphalerite (wurtzite), and limonite, and the barren minerals are tremolite, silica, talc, siderite, calcite, and some iron aluminosilicates. Regarding the dis- tribution of non-ferrous metals, it should be noted that, in contrast to copper and zinc, cobalt does not form its own mineral forms, and in the amount up to 0.35 mass% it is isomorphically included in pyrite. It follows from the HTXRD data that there were no sig- nificant changes in the phase composition of the initial sam- ple before 200 °C; only at 200 °C the appearance of iron (III) sulfate (Fe2(SO4)3) was noted, indicating the beginning of pyrite oxidation by the following reaction: 2FeS2 + 7O2 = Fe2(SO4)3 + SO2, logK473 = 229. (11) The fact of low-temperature pyrite oxidation agrees with the data [15, 52]. The formation of hexagonal pyrrho- tite (Fe9S10), poitevinite (FeSO4·H2O), and copper (II) sul- fate (CuSO4) at 300 °C can be associated with the processes described by the following equations: 9FeS2 + 8O2 = Fe9S10 + 8SO2, logK573 = ~18, (12) FeS2 + 3O2 = FeSO4 + SO2, logK573 = 80, (13) CuFeS2 + 4O2 = FeSO4 + CuSO4, logK573 = 100, (14) FeSO4 + H2O = FeSO4·H2O, logK573 = –1. (15) In this case, the reason for the appearance of hydrate compounds may be the interaction of oxidation products with water contained in the air, released during the dehydra- tion of rock-forming minerals. At 400 °C, in addition to the phases formed at 300 °C, monoclinic pyrrhotite (Fe7S8), cubanite (CuFe2S3), magnetite (Fe3O4), and hematite (Fe2O3) were detected, formed by the reactions listed below [15]: 7FeS2 + 6O2 = Fe7S8 + 6SO2, logK673 = 122, (16) 2FeS2 + 5.5O2 = Fe2O3 + 4SO2, logK673 = 121, (17) 3FeS2 + 8O2 = Fe3O4 + 6SO2, logK673 = 176, (18) 4Fe3O4 + O2 = 6Fe2O3, logK673 = 23, (19) 2CuFeS2 + 3.5O2 = 2CuS + Fe2O3 + 2SO2, logK673 = 76, (20) CuS + 2FeS2 = CuFe2S3 + S2. (21) Despite the fact that the presence of pyrite in the roast- ing product at 400 °C was not confirmed, its reflections re- appear at 500 °C; the other newly formed phases are hexag- onal modifications of iron sulfide with the formulae of Fe11S12 and FeS, dolerophanite (CuO·CuSO4), and tenorite (CuO); in this regard the oxidation chemistry can be supplemented with the following set of equations [15, 50]: 11FeS2 + 10O2 = Fe11S12 + 10SO2, logK773 = ~18, (22) FeS2 + O2 = FeS + SO2, logK773 = 18, (23) Fe7S8 + 15O2 = 7FeSO4 + SO2, logK773 = 281, (24) Fe7S8 + 13.25O2 = 3.5Fe2O3 + 8SO2, logK773 = 257, (25) Fe9S10 + 16O2 = 3Fe3O4 + 10SO2, (26) 3FeS + 5O2 = Fe3O4 + 3SO2, logK773 = 97, (27) 2CuFeS2 + 6.5O2 = 2CuO + Fe2O3 + 4SO2, logK773 = 109, (28) 2CuFeS2 + 4.5O2 = Cu2S + Fe2O3 + 3SO2, logK773 = 64, (29) Cu2S + 2O2 = 2CuO + SO2, logK773 = 17, (30) 2CuFeS2 + 7O2 = CuO·CuSO4 + Fe2O3 + 3SO2, logK773 = 116, (31) CuFe2S3 + 5O2 = CuO + Fe2O3 + 3SO2. (32) Reaching 600 °C is characterized by the complete con- sumption of iron and copper sulfides with the formation of hematite and magnetite, iron (II) and (III) and copper (II) sulfates according to reactions (13), (14), (24)–(30), and also by the appearance of wustite (Fe0.902O), which is formed according to the reaction: FeS2 + 2.554O2 = 1.109Fe0.902O + 2SO2, logK873 = ~40. (33) Starting from 700 °C, the products of roasting show the ab- sence of sulfates, which is associated their decomposition [15, 20, 27, 31–33, 50, 52, 82]: 2FeSO4 = Fe2O3 + SO3 + SO2, logK973 = ~0, (34) Fe2(SO4)3 = Fe2O3 + 3SO3, logK973 = –2, (35) https://doi.org/10.15826/chimtech.2023.10.2.02 https://doi.org/10.15826/chimtech.2023.10.2.02 Chimica Techno Acta 2023, vol. 10(2), No. 202310202 ARTICLE 6 of 12 DOI: 10.15826/chimtech.2023.10.2.02 4CuSO4 + Cu2S = 6CuO + 5SO2, logK973 = 7, (36) 4CuSO4 + Cu2O = 3CuO·CuSO4 + SO2, logK973 = 0.5 (37) 4CuO·CuSO4 + Cu2S = 10CuO + 5SO2, logK973 = 5, (38) 2CuSO4 = CuO·CuSO4 + SO3, logK973 = –2, (39) CuO·CuSO4 = 2CuO + SO3, logK973 = –2. (40) The products of sulfide oxidation in this case are wus- tite, magnetite and hematite, as well as copper (I) ferrite (CuFeO2), which appears as a result of the attack of mag- netite on copper (II) oxide: CuO + Fe3O4 = 2CuFeO2 + Fe2O3, logK973 = 2. (41) At the same temperature, one can expect the onset of intensive thermal decomposition of hydrated magnesium silicates, for example, chrysotile (Mg3Si2O5(OH)4) and talc (Mg3Si4O10(OH)2), leading to the formation of metasilicates, in particular diopside (CaFe0.13Mg0.943Si1.927O6); these pro- cesses can be represented by a general scheme [83]: Mg3Si2O5(OH)4 = Mg2SiO4 + MgSiO3 + 2H2O, logK973 = 3, (42) Mg3Si4O10(OH)2 = 3MgSiO3 + SiO2 + H2O, logK973 = 0.5. (43) The absence of traces of forsterite (Mg2SiO4) in the cor- responding diffractograms may be due to its amorphous- ness at the initial moments of formation. Also, at 700 °C, reflections from zincite (ZnO) formed according to the fol- lowing equation were detected [29]: ZnS + 1.5O2 = ZnO + SO2, logK973 = 20. (44) At 800 and 900 °C, the final products of deep roasting are formed containing hematite (Fe2O3), magnetite (Fe3O4), and diopside (Fe0.015Mg0.985SiO3 at 800 °C and Fe0.15Mg1.82Si2O6 at 900 °C), which originate in the above reactions. At 800 °C, franklinite (ZnFe2O4) and copper fer- rite of the composition CuFe5O8 can additionally be formed, and at 900 °C – zinc silicate (ZnSiO3), tenorite (CuO), and delafossite (CuFeO2); the first three of these phases are the products of the following reactions [29, 63, 84]: ZnO + Fe2O3 = ZnFe2O4, logK1073 = 1, (45) CuFeO2 + 2Fe2O3 = CuFe5O8, (46) ZnO + SiO2 = ZnSiO3, logK1173 = ~0, (47) Where the last two are the processes described by equations (28) and (41). The composition of the gas phase in the con- sidered temperature range is determined by the reaction 2SO2 + O2 = 2SO3, logK1053 = ~0, (48) whose direction changes from direct to reverse at ~780 °C. It should also be noted that the absence of siderite and zinc sulfide reflections in a number of diffractograms in the temperature ranges of their possible existence can be ex- plained by the low sensitivity of the applied analytical method with respect to these phases. The values of the equi- librium constants of most of the listed reactions exceed (or are close to) unity, which confirms the possibility of their proceeding in the forward direction (reactions for which, due to the lack of thermodynamic data for a number of com- pounds in the HSC Chemistry 6.12 package, the KT value is not indicated, are hypothetical or confirmed by literature data). On the whole, the presented reactions can only serve as the simplest explanation for the appearance of phases detected by XRD in the roasting products; it is obvious that the chemistry of the ore oxidation is even more complex. The results of thermal analysis of the ore carried out un- der heating conditions from 30 to 1100 °C in air flow (30 cm3·min–1) with heating rates of βi = 5, 10, and 20 °C·min–1 is presented in Figures 2 and 3, and Table 1. There are three primary thermal effects on the DSC curves (Figure 2). The first effect is a complex exothermic peak of high intensity formed by a series of partially overlapping (partially resolved at βi = 5 °C·min–1) elementary exothermic peaks. The separation of complex exothermic peaks showed (Figure 3 and Table 1) that each of them is the result of the superimpostion of five elementary exothermic peaks (here- inafter referred to as EP1, EP2, EP3, EP4, and EP5). The sec- ond and third effects are weakly expressed simple (elemen- tary) endothermic peaks (hereinafter referred to as EP6 and EP7). According to the TG data (Figure 2), by 1100 °C the total mass loss during oxidation is 28–29%, of which the 30– 318 °C region free of DSC effects accounts for 4–5%, and the series of exothermic (359–570 °C) and two endothermic (561–664 °C and 743–927 °C) anomalies are 7–10, 8–9, and, 4–6% respectively; the remaining losses account for the high-temperature region. Figure 2 TG and DSC curves (βi = 5, 10, and 20 °C·min –1) for the pyritic copper ore. https://doi.org/10.15826/chimtech.2023.10.2.02 https://doi.org/10.15826/chimtech.2023.10.2.02 Chimica Techno Acta 2023, vol. 10(2), No. 202310202 ARTICLE 7 of 12 DOI: 10.15826/chimtech.2023.10.2.02 Figure 3 Separation results for complex exothermic DSC peaks. Solid straight lines are baselines, dots are experimental DSC data, dashed curves are calculated DSC curves for elementary peaks, and solid curves are summary calculated DSC curves. The circles with arrows show the numbers of elementary peaks. Table 1 Parameters of the elementary DSC peaks, and nij values calculated by the Augis–Bennett method. Parameter Value βi = 5 °C·min –1 Peak EP1 EP2 EP3 EP4 EP5 EP6 EP7 Toij/°C 413 397 442 449 451 561 743 Tpij/°C 415 417 447 467 484 598 774 Teij/°C 418 426 457 486 514 629 834 ΔTpij/K 3.1 16.3 12.6 23.8 14.0 32.2 43.5 nij 2.5 1.6 1.5 1.2 2.8 1.8 3.4 βi = 10 °C·min –1 Peak EP1 EP2 EP3 EP4 EP5 EP6 EP7 Toij/°C 416 394 442 478 483 566 760 Tpij/°C 420 422 466 496 513 615 814 Teij/°C 426 443 494 527 546 645 867 ΔTpij/K 5.7 28.7 30.8 27.9 37.1 38.3 33.6 nij 1.4 0.9 0.7 1.2 1.2 1.6 4.7 βi = 20 °C·min –1 Peak EP1 EP2 EP3 EP4 EP5 EP6 EP7 Toij/°C 398 431 440 433 489 596 798 Tpij/°C 427 450 462 496 536 630 855 Teij/°C 445 488 498 549 562 664 927 ΔTpij/K 26.8 31.9 33.9 38.1 42.4 31.4 42.5 nij 0.3 0.9 0.6 0.8 1.1 1.8 4.0 Theoretical calculations demonstrated that the removal of all volatile components (H2O, CO2, and S) into the gas phase should reduce the mass of the sample by ~20%; the experimental estimate exceeds this value, indicating either a possible error in determining the material composition of the ore or a more complex process. The zone of exothermic processes is confined to the traces of intense gas emission noted on the MS curves (Figure 4): SO2 (TpSO2 = 415 and 466 °C at βi = 5 °C·min–1, TpSO2 = 420 and 465 °C at βi = 10 °C·min–1, and TpSO2 = 427 and 456 °C at βi = 20 °C·min–1), SO3 (TpSO3 = 415 °C and 464 °C at βi = 5 °C·min–1, TpSO3 = 419 and 472 °C at βi = 10 °C·min–1, and TpSO3 = 463 °C at βi = 20 °C·min–1), and CO2 (TpCO2 = 519 °C at βi = 5 °C·min–1, TpCO2 = 536 °C at βi = 10 °C·min–1, and TpCO2 = 546 °C at βi = 20 °C·min–1). https://doi.org/10.15826/chimtech.2023.10.2.02 https://doi.org/10.15826/chimtech.2023.10.2.02 Chimica Techno Acta 2023, vol. 10(2), No. 202310202 ARTICLE 8 of 12 DOI: 10.15826/chimtech.2023.10.2.02 Subsequent endothermic events are associated with peaks in the SO2 ion current (TpSO2 = 604 and 819 °C at βi = 5 °C·min–1, TpSO2 = 632 and 842 °C at βi = 10 °C·min–1, and TpSO2 = 647 and 855 °C at βi = 20 °C·min–1). The MS traces also revealed three weak peaks of the ion current of water, the maxima of which (TpH2O) vary in the ranges of 120–125, 290–310, and 950–960 °C. Analysis of the results of HTXRD, DSC, TG, and MS shows that heating (βi = 5–20 °C·min–1) of the pyritic cop- per ore up to 318 °C is accompanied by the removal of ad- sorption (capillary) and hygroscopic moisture into the gas phase, which is associated with the initial monotonic mass loss (Δm = 4–5%) and the release of the H2O into the gas phase at 120–125 and 290–310 °C. The main oxidation pe- riod of pyritic copper ore, associated with the release of the largest (–ΔH = 1468–2052 J·g–1) amount of heat, begins at 359 °C, culminates at 420–468 °C, and finished at 570 °C; it accounts for up to ~34 relative % total mass loss. Numerous interactions of the ore minerals with a gase- ous atmosphere can occur within its boundaries, described by equations (12)–(32); some reactions are characterized by a high thermal effect and provide for the release of a large amount of SO2 capable of interacting with O2 by reaction (48). The appearance of CO2, intensifying at 519–546 °C, can be associated with the oxidative decomposition of si- derite: 4FeCO3 + O2 = 2Fe2O3 + 4CO2, logK819 = 40. (49) Based on the fact of the absence of mass increase re- vealed by the TG method, the main processes in this tem- perature range can be associated with ignition and direct oxidation (burning) of sulfides with the formation of oxides [15]; the formation of sulfates is limited, or they are effec- tively broken by sulfide compounds. The final stage of the oxidation includes two processes accompanied by weak en- dothermic effects (ΔH = 49–97 and 51–113 J·g–1, respec- tively), mass reduction (up to ~31 and ~21 relative %, re- spectively), and SO2 release; apparently, in this case, ther- mal decomposition of residual sulfates takes place: iron sul- fates at 561–664 °C (reactions (34) and (35)) and copper sulfates at 743–927 °C (reactions (39) and (40)). This con- clusion is confirmed by the literature data [19, 31, 57, 86, 87]. At 950–960 °C, part of the crystallization water of rock-forming silicate minerals is released. Thus, the kinetics of oxidative roasting of the ore can be formally attributed to seven elementary reactions: five ex- othermic (at 398–445, 394–488, 440–498, 433–549, and 451–562 °C) corresponding to intensive burning of iron, copper and zinc sulfides, and two endothermic (at 561– 664 °C and 743–927 °C) related to the decomposition of re- sidual copper and iron sulfates. The grouped DSC peaks of the same name, which are their traces, are shown in Figure 5. The results of kinetic analysis of the DSC data in relation to the temperature ranges of these reactions are presented in Figures 6, and 7, and Table 2. The shape of the plots of the yij(αij) function (Figure 7) for elementary oxidation reactions corresponds to the JMAEK (An) kinetic model of nucleation and crystal growth [78]. The refined invariant kinetic parameters of the elemen- tary reactions differ somewhat from the initial estimates (Table 2). Figure 4 MS curves (βi = 20 °C·min –1) for the pyritic copper ore. Figure 5 Grouping results for elementary endothermic DSC peaks (Results for exothermic elementary DSC peaks have a similar view). Figure 6 Kissinger plots for elementary DSC peaks. https://doi.org/10.15826/chimtech.2023.10.2.02 https://doi.org/10.15826/chimtech.2023.10.2.02 Chimica Techno Acta 2023, vol. 10(2), No. 202310202 ARTICLE 9 of 12 DOI: 10.15826/chimtech.2023.10.2.02 The kinetic models derived from these parameters have the following form: dα1 d𝑡 = 4.89 ∙ 1031 exp (– 459000 𝑅𝑇 ) (1 – α1) [– ln(1 – α1)] 0.29, (50) dα2 d𝑡 = 4.52 ∙ 108 exp (– 140000 𝑅𝑇 ) (1 – α2) [– ln(1 – α2)] 0.09, (51) dα3 d𝑡 = 4.74 ∙ 1013 exp (– 220000 𝑅𝑇 ) (1 – α3), (52) dα4 d𝑡 = 1.32 ∙ 108 exp (– 160000 𝑅𝑇 ) (1 – α4) [– ln(1 – α4)] 0.09, (53) dα5 d𝑡 = 1.24 ∙ 106 exp (– 155000 𝑅𝑇 ) (1 – α5) [– ln(1 – α5)] 0.41, (54) dα6 d𝑡 = 5.88 ∙ 1015 exp (– 320000 𝑅𝑇 ) (1 – α6) [– ln(1 – α6)] 0.17, (55) dα7 d𝑡 = 1.69 ∙ 104 exp (– 149000 𝑅𝑇 ) (1 – α7) [– ln(1 – α7)] 0.17, (56) Verification of the obtained models showed a high (ravj = 0.8580–0.9984) level of correlation between the refined calculated and experimental data (Figure 8, and Table 2). Therefore, these models describe the kinetic patterns of ox- idation of the investigated pyritic copper ore under given conditions with sufficient reliability. According to the literature data, the effective activation energy of the processes accompanying the oxidation (when heated in air) of iron, copper, and zinc sulfides, as well as their natural and artificial mixtures of various sizes (from –0.043 to –12 mm), can be of 7–463 kJ·mol–1 [11, 14, 19, 26, 27, 40, 41, 53, 60, 67, 69, 72, 82, 85]; the estimates obtained in this work (Erj = 124–455 kJ·mol–1) do not go beyond this range. The results of determining the reaction model show that the limiting step of all elementary oxidation reactions of the studied ore is nucleation and crystal growth. The ex- amples of the application of the JMAEK model to describe the mechanism of oxidation of sulfides (in particular, chal- copyrite and pyrite concentrates) should be mentioned [41, 67, 88]. The values of the Avrami exponent (nrj) obtained in this work are in the range from 1 to 1.7, which allows us to draw the following conclusions regarding the details of the mechanism and morphological features of the process: i) crystallization of the products of elementary reactions is accompanied by an increase in the number of nuclei; ii) nuclei of a new phase may be formed both at the inter- face and in the volume of the ore particles; iii) crystal growth is one-dimensional and controlled by a chemical re- action at the phase boundary or diffusion of reagents [89]. Figure 7 Master plots y(α) for endothermic elementary reactions (Results for exothermic elementary reactions have a similar view). Figure 8 Experimental (circles) and refined calculated (triangles) kinetic curves for endothermic elementary reactions (Results for exothermic elementary reactions have a similar view). Table 2 Kinetic parameters of elementary reactions. Elementary reaction Kinetic parameter Ej/kJ·mol –1 Erj/kJ·mol –1 logAj/log(s –1) logArj/log(s –1) nj n r j ravj 1 455±22 459 32.5 31.5 1.4 1.4 0.8615 2 142±21 140 8.3 8.6 1.1 1.1 0.8580 3 220±22 220 13.7 13.7 1.0 1.0 0.9464 4 159±21 160 8.7 8.1 1.1 1.1 0.9527 5 124±20 155 5.9 5.9 1.7 1.7 0.9928 6 275±15 320 15.6 15.7 1.7 1.2 0.9984 7 154±14 149 4.4 4.2 4.0 1.2 0.9689 Note. The numbers of elementary reactions correspond to the numbers of elementary peaks in Table 1. https://doi.org/10.15826/chimtech.2023.10.2.02 https://doi.org/10.15826/chimtech.2023.10.2.02 Chimica Techno Acta 2023, vol. 10(2), No. 202310202 ARTICLE 10 of 12 DOI: 10.15826/chimtech.2023.10.2.02 It should be noted that, compared with copper concen- trates, pyritic copper ore is a material that is more tech- nologically complex, and the purpose of its roasting is not only the removal of a certain amount of sulfur into the gas phase, but also the corresponding transformation (decom- position and dehydration) of rock-forming minerals. 4. Limitations For deeper understanding of the kinetics of solid-state oxi- dation of the studied sulfide systems, it is necessary to ver- ify the data obtained in this work with the results of study- ing the isothermal kinetics of the process and information about the microstructure of the oxidation products. 5. Conclusions The formal kinetics of the solid-state oxidation of iron, cop- per and zinc sulfide natural mixture, typical of the pyritic copper ores, can be attributed to seven elementary reac- tions: five exothermic (at 398–445, 394–488, 440–498, 433–549, and 451–562 °C), corresponding to intensive burning of iron, copper and zinc sulfides, and two endother- mic (at 561–664 and 743–927 °C), related to the decompo- sition of residual copper and iron sulfates. The limiting steps of these reactions are nucleation and crystal growth, and the values of activation energy, pre-ex- ponential factor and Avrami exponent are in the ranges of 140–459 kJ·mol–1, 1.41·104–3.49·1031 s–1, and 1.0–1.7, respec- tively. Crystallization of the products of elementary reac- tions is accompanied by an increase in the number of nu- clei; nuclei of a new phase may be formed both at the inter- face and in the volume of the ore particles, and crystal growth is one-dimensional and controlled by a chemical re- action at the phase boundary or diffusion. The resulting kinetic models make it possible to predict a degree of process completion depending on time and tem- perature. The results of the work as a whole can contribute to the development of theoretical ideas about the physico- chemical transformations of pyrite ores and concentrates during pyrometallurgical operations, and can also be used in the practice of oxidative roasting of these materials. ● Supplementary materials No supplementary materials are available. ● Funding This research had no external funding. ● Acknowledgments The work was carried out according to the State Assignment for IMET UB RAS (No. 122020100404-2) using equipment of the Collaborative usage center "Ural–M". ● Author contributions Conceptualization: A.M.K. Methodology: A.M.K. Formal analysis: A.M.K. Investigation: R.I.G. and S.M.P. Writing – original draft preparation: A.M.K. Writing – review and editing: R.I.G. ● Conflict of interest The authors declare no conflict of interest. ● Additional information Author IDs: Alexander M. Klyushnikov, Scopus ID 57220987625; Sergey M. Pikalov, Scopus ID 6603186623; Roza I. Gulyaeva, Scopus ID 6602478183. Website: Institute of Metallurgy of the Ural Branch of the Russian Academy of Sciences, http://www.imet-uran.ru. References 1. Schlesinger ME, King MJ, Sole KC, Davenport WG. Extractive Metallurgy of Copper. 5th Edition. Oxford: Elsevier; 2011. 2. Selivanov EN, Gulyaeva RI, Klyushnikov AM. Study of struc- ture and phase composition of copper-cobalt sulfide ores of Dergamyshskoe deposit. Tsvetnye Metally. 2016;3:13–17. doi:10.17580/tsm.2016.03.02 3. Melekestseva IYu, Maslennikov VV, Maslennikova SP. Trace- elements in sulfides of the Dergamysh cobalt-bearing massive sulfide deposit, the Southern Urals: Mode of occurrence and matter sources. Lithosphere (Russia). 2020;20(4):499–516. doi:10.24930/1681-9004-2020-20-4-499-516 4. Nagaeva SP, Mezentseva OP, Kozorez MV. Mineralogical re- searches of copper cobalt-containing ores of Dergamysh de- posit. Gornyi Zhurnal/Mining J. 2014;11:31–4. 5. 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