Unified Phase Diagram and Competition-Coupling Mechanism for Pyrite Thermal Transformation

Abstract

The thermal transformation mechanism of pyrite in coal, which governs sulfur emissions and ash deposition, remains highly controversial. There are significant discrepancies in reported activation energies (E_a) (60–310 kJ/mol) and conflicting reaction pathways. To resolve these long-standing controversies, this study proposes a competition-coupling mechanism: pyrolysis and oxidation compete under local O₂ and temperature gradients, while coupling through microstructural evolution. Specifically, pyrolysis generates a porous Fe_1−XS that facilitates oxidation, which in turn can form a passivating oxide/sulfate layer that promotes further pyrolysis. This mechanism reconciles longstanding kinetic controversies by showing that the apparent activation energy is not a fixed value but instead a dynamic parameter, shifting along a continuous curve that bridges pyrolysis and oxidation-dominated regimes. Furthermore, we construct a unified phase diagram by incorporating the competition-coupling mechanism into classical thermodynamic equilibria. This diagram uses the molar ratio FeS₂/(FeS₂ + O₂) and temperature to categorize the transformation process into four distinct regions—pyrolysis-dominated, competition-coupling, oxidation-dominated, and melt-dominated. The key contribution of this work lies in the diagram which offers a practical framework for optimizing combustion and roasting systems, allowing for improved control over sulfur emissions and ash-related issues such as slagging and fouling.

1. Introduction

Pyrite (FeS₂), the most abundant sulfide mineral in coal, governs the formation of sulfur and iron oxides during thermal transformation. These products are primary contributors to air pollution, boiler corrosion, as well as ash slagging and deposition [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Therefore, a fundamental and predictive understanding of the FeS₂ transformation mechanism is essential for advancing clean coal utilization technologies.

Although considerable research has been conducted on pyrolysis and oxidation over the past several decades [7,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33], most studies have traditionally analyzed them as isolated processes, failing to reveal their complex interactions under non-equilibrium conditions. Consequently, the dominant reaction pathways and kinetic parameters remain contentious, as reflected in the wide range of reported apparent activation energies (60–310 kJ/mol).

To resolve these controversies fundamentally, we isolate the behavior of pyrite from the complexities of the coal matrix and then (1) reevaluate the thermodynamic boundaries of FeS₂ transformation, (2) reconcile the discrepant kinetic data by identifying reaction mechanisms, (3) propose a unified competition-coupling mechanism, and (4) construct an original phase diagram.

By mapping the competition-coupling mechanism onto a modified thermodynamic diagram, this work yields a unified and predictive framework for FeS₂ transformation, which has direct implications for controlling sulfur emissions and ash issues in coal utilization technologies.

2. Re-Evaluating the Thermodynamic Boundaries

2.1. Analysis of Reported Phase Equilibria

Reported thermodynamic phase diagrams for pyrite transformation exhibit considerable diversity, as they are derived from different subsystems (e.g., Fe-O, Fe-S, or Fe-S-O) and rely on different state variables (e.g., temperature, composition, or gas partial pressures). Through an integrative analysis, we establish three governing principles for phase stability in the Fe-S-O system:

1.

Collaborative Control of Temperature and Oxygen Partial Pressure (pO₂):

Within the Fe-O subsystem, the work of Darken and Gurry (1946) [34] established the sequence of stable phases transitioning from Fe₂O₃→Fe₃O₄→FeO with increasing temperature and decreasing pO₂.

In the more complex Fe-S-O system, the works of Jorgensen and Moyle (1982) [17] and Zhang et al. (2019) [35] further demonstrate that sulfates (FeSO₄ and Fe₂(SO₄)₃) emerge as key metastable phases at lower temperatures and under high pSO₂ conditions.

Furthermore, within the FeS-FeO and FeO-Fe₂O₃ subsystems, McLennan et al. [28] demonstrated the following pathway: FeS₂→Fe_1−XS→FeS-FeO eutectic melt under reducing conditions and FeS₂→Fe_1−XS→FeO→Fe₃O₄→Fe₂O₃ under oxidation conditions.

2.

Non-Stoichiometry of Pyrrhotite (Fe_1−XS):

In the Fe-S subsystem, the phase diagrams from Waldner and Pelton (2005) [36] and Lambert et al. (1998) [37] clarify that pyrrhotite (Fe_1−XS) is an non-stoichiometric phase. Its composition (the value of x) is a function of both temperature and sulfur vapor pressure (pS₂). For instance, FeS₂ pyrolysis to FeS_X occurs at 988 °C in a system composed of Fe and FeS_X, while the pyrolysis temperature decreases to 743 °C in a system composed of FeS₂ and FeS_X.

3.

Existence of Key Phase Transition Temperatures:

In the Fe-S system, FeS₂ pyrolysis initiates below 400 °C, producing non-stoichiometric Fe_1−XS and sulfur vapor (S₂). While within the (Fe + FeS) phase, Fe_1−XS transforms via a peritectic reaction into liquid phase (liquid) and fcc-Fe at 910–988 °C [36,38,39,40,41,42,43]. Conversely, within (Fe_1−XS + FeS₂) phase, FeS₂ directly pyrolyzes into Fe_1−XS and sulfur vapor (S₂) at 743 °C. Upon further heating to 1180 °C, this Fe_1−XS melts into a sulfur-rich liquid, releasing additional sulfur vapor (S₂) [36,38,39,40,41,42,43].

In the Fe-S-O system, a sequence of oxide formations occurs: Fe₂O₃ forms directly below 404 °C, with Fe₃O₄ as an intermediate phase stable between 404 °C and 552 °C. Sulfates, including FeSO₄ and Fe₂(SO₄)₃, are stable below 583 °C and 644 °C, respectively. At elevated temperatures, FeO melts at 1370–1424 °C, Fe₃O₄ melts at 1424–1597 °C, and Fe₂O₃ melts at around 1565 °C [28,34]. Notably, FeO is only stable under specific high-temperature, low-oxygen conditions.

Despite the delineation of these “thermodynamically feasible” pathways, significant discrepancies persist between these equilibrium predictions and experimental observations. This gap arises because equilibrium assumptions neglect several critical kinetic factors:

• Local Atmospheric Conditions:

The gas composition (pO₂ and pS₂) at the particle surface can deviate drastically from the particle pores or at the reaction interface, which is influenced by gas flow rate, particle packing density, and heating rate.

• Influence of Mineral Occurrence Mode:

For instance, the oxidation of coal-matrix-encapsulated FeS₂ is significantly delayed, as oxygen must first diffuse through the coke layer.

• Intra-Particle Temperature Gradients:

During rapid heating, a substantial temperature difference of 50–100 °C [16] exists between the particle exterior and interior, causing the surface and the core to follow different transformation pathways.

2.2. Thermodynamic Driving Force: Calculation Δ_rG^θ

We evaluated the Gibbs free energy change (Δ_rG^θ) for 24 major FeS₂ transformation reactions, using data from Zhang et al. [35] to compare the thermodynamic feasibility of pyrolysis and oxidation pathways.

The data in

Table 1. Possible chemical reactions and corresponding Δ_rG^θ at temperatures of 500 and 1000 K. (Data source: Zhang et al. [35].)

No.	Reaction	Equation	ΔrGθ at 500 K kJ/mol	ΔrGθ at 1000 K kJ/mol
1	FeS2 = 8/7Fe0.875S + 3/7S2(g)	−0.1219 T + 109.0817	48.13	−12.82
2	FeS2 = FeS + 1/2S2(g)	−0.1375 T + 140.2344	71.48	2.73
3	S + 2O2 = 2SO2	0.1465 T − 723.7860	572.48	1003.73
4	FeS2 + 11/4O2(g) = 1/2Fe2O3 + 2SO2(g)	0.0756 T − 832.7516	−794.95	−757.15
5	FeS2 + 7/4O2(g) = 1/2Fe2O3 + SO2(g)	0.1407 T− 611.2840	−540.93	−470.58
6	FeS2 + 8/3O2(g) = 1/3Fe3O4 + 2SO2(g)	0.0519 T − 792.2288	−766.28	−740.33
7	FeS2 + O2(g) = FeS + SO2(g)	−0.0647 T − 221.4677	−253.82	−286.17
8	FeS2 + 6/7O2(g) = 8/7Fe0.875S + 6/7SO2(g)	−0.0592 T − 201.0982	−230.70	−260.30
9	FeS2 + 3O2(g) = FeSO4 + SO2(g)	0.2920 T − 1050.5365	−904.54	−758.54
10	FeS2 + 7/2O2(g) = 1/2Fe2(SO4)3 + SO2(g)	0.4859 T − 1265.3779	−1022.43	−779.48
11	Fe0.875S + 53/32O2(g) = 7/16Fe2O3 + SO2(g)	0.1192 T − 553.6720	−494.07	−434.47
12	Fe0.875S + 19/12O2(g) = 7/24Fe3O4 + SO2(g)	0.0985 T − 518.6612	−469.41	−420.16
13	Fe0.875S + 1/8O2(g) = 7/8FeS + 1/8SO2(g)	−0.038 T − 18.0233	−37.02	−56.02
14	Fe0.875S + O2(g) = 7/8FeSO4 + 1/8SO2(g)	0.3099 T − 744.6433	−589.69	−434.74
15	Fe0.875S + 47/16O2(g) = 7/16Fe2(SO4)3 + 5/16SO2(g)	0.4938 T − 1127.0820	−880.18	−633.28
16	FeS + 5/3O2(g) = 1/3Fe3O4 + SO2(g)	0.1166 T − 570.7611	−512.46	−454.16
17	FeS + 2O2(g) = FeSO4	0.3566 T − 829.0689	−650.77	−472.47
18	FeS + 5/2O2(g) + 1/2SO2(g) = 1/2Fe2(SO4)3	0.5505 T − 1043.9102	−768.66	−493.41
19	Fe3O4 + 1/4O2(g) = 3/2Fe2O3	0.0722 T − 121.5684	−85.47	−49.37
20	Fe3O4 + O2(g) + 3SO2(g) = 3FeSO4	0.7201 T − 774.9232	−414.87	−54.82
21	Fe3O4 + 5/2O2(g) + 9/2SO2(g) = 3/2Fe2(SO4)3	1.3018 T − 1419.4472	−768.55	−117.65
22	Fe2O3 + 1/2O2(g) + 2SO2(g) = 2FeSO4	0.4319 T − 435.5699	−219.62	−3.67
23	Fe2O3 + 3/2O2(g) + 3SO2(g) = Fe2(SO4)3	0.8197 T − 865.2525	−455.40	−45.55
24	FeSO4 + 1/2O2(g) + 1/2SO2(g) = 1/2Fe2(SO4)3	0.1939 T − 214.8413	−117.89	−20.94

lead to two key conclusions.

First, at 500 K, sulfate formation is the most thermodynamically favored pathway, as indicated by the highest negative Δ_rG^θ value for Reactions 9 and 10. This is followed by direct oxidation to Fe₃O₄ and Fe₂O₃ (Reaction 4–6). The oxidation of Fe_1−XS to Fe₂(SO₄)₃ is also more favorable than its oxidation to iron oxides, as seen by comparing the Δ_rG^θ of Reactions 11–12, 14–15, and 17–18. In contrast, the pyrolysis of FeS₂ to Fe_1−XS or FeS (Reactions 1–2 and 7–8) is the least favored, exhibiting the highest Δ_rG^θ values at 500 K and 1000 K, confirming its non-spontaneous nature. However, at 1000 K, the thermodynamic favorability of sulfate formation decreases, becoming comparable to that of oxide formation.

Second, FeS₂ pyrolysis is endothermic (Δ_rH > 0), imposing a significant energy barrier. In contrast, oxidation reactions are exothermic (Δ_rH < 0), which promotes self-heating and consequently accelerates reaction kinetics. This establishes that oxidation is both thermodynamically and kinetically preferable over pyrolysis.

However, this thermodynamic preference for oxidation relies on the assumption of sufficient oxygen supply to the reaction front. In the case that oxygen diffusion is limited (e.g., within large particles or under low bulk O₂ concentrations), the oxidation process becomes kinetically hindered, potentially leading to pyrolysis instead.

2.3. Calculation of Thermodynamic Phase Diagram

The thermodynamic equilibrium calculations were performed using FactSage software (v8.4) with its associated databases (FToxid, FTsulf, and FactPS). These databases were selected for their comprehensive coverage of oxides, sulfides, and gaseous species, ensuring their suitability for simulating the high-temperature Fe-S-O system. The corresponding results are presented in Figure 1. The Y-axis represents temperature. The X-axis is defined by the initial molar ratio of FeS₂/(FeS₂ + O₂), which quantitatively represents the reaction front redox environment.

1.

For FeS₂/(FeS₂ + O₂) < 28.6% area (i.e., N (FeS₂)/N (O₂) < 0.4:1):

Below 1456 °C, the dominant phase is Fe₂O₃.

Between 1400 and 1580 °C, Fe₃O₄ is the primary product.

Above 1580 °C, liquid phase is the major phase.

2.

For 28.6% < FeS₂/(FeS₂ + O₂) < 47.1% area (i.e., 0.4:1 < N (FeS₂)/N (O₂) < 0.89:1):

Below 480 °C, the dominant phase is Fe₂O₃.

Between 480 and 1069 °C, Fe₃O₄ is the primary product.

Above 1069 °C, liquid phase is the major phase.

3.

For 47.1% < FeS₂/(FeS₂ + O₂) < 60% area (i.e., 0.89:1 < N (FeS₂)/N (O₂) < 1.5:1):

Below 1069 °C, the dominant phase is Fe₃O₄.

Above 1069 °C, the primary product is liquid phase.

4.

For 60% < FeS₂/(FeS₂ + O₂) < 100% area (i.e., 1.5:1 < N (FeS₂)/N (O₂) < ∞):

Below 563 °C, the dominant phase is Fe₃O₄.

Between 563 and 947 °C, pyrolysis becomes dominant, and FeS is the primary product.

Above 947 °C, the primary product is liquid phase.

5

Sulfate area:

Fe₂(SO₄)₃ is identified as an oxidation product at temperatures below approximately 600–700 °C for FeS₂/(FeS₂ + O₂) < 26.7% (i.e., N (FeS₂)/N (O₂) < 0.36:1).

FeSO₄ is observed as an oxidation product at temperatures below 395 °C for FeS₂/(FeS₂ + O₂) = 26.5%–47.1% (i.e., N (FeS₂)/N (O₂) = 0.36:1 to 0.89:1).

Although thermodynamic analysis accurately predicts the stable equilibrium phases, the actual transformation pathways are kinetically controlled and exhibit more complex behavior. The following section reanalyzes the kinetic data to explain the discrepancies between these thermodynamic predictions and the experimental observations.

3. Reconciling Discrepant Kinetic Data

3.1. Reinterpreting Pyrolysis Mechanisms and E_a

The kinetics of the pyrolysis process are governed by two primary rate-controlling steps: (1) intrinsic chemical reaction control and (2) product layer diffusion control (apparent kinetics). Additionally, two-stage or transitional state models have also been proposed to describe more complex behavior.

1.

Chemical Reaction Controlled Model (Intrinsic)

The chemical reaction control mechanism dominates when sulfur vapor (S₂) is rapidly and completely removed from the reaction interface, as occurs with coarse-grained or plate-like FeS₂ particles in a high-flow inert atmosphere. This S-S bond-breaking process involves a high intrinsic activation energy barrier.

Morphologically, this process produces an “unreacted core-porous shell” structure, where the porous Fe_1−XS shell results from S₂ vapor release, continually exposing fresh FeS₂ surface at the advancing reaction front [13,25,41,44,45,46,47,48,49,50,51,52,53,54,55,56,57].

2.

Diffusion Controlled Model (Apparent)

In experiments employing fine particles or under low-flow/static inert atmospheres (e.g., conventional Thermogravimetric Analysis, also called TGA), the rapidly released S₂ accumulates due to inefficient convective removal. Consequently, the rate-limiting step shifts to the diffusion of accumulated S₂ through the porous Fe_1−XS product layer. This diffusion-controlled process exhibits a lower apparent activation energy, E_a, typically falling within the range of 90–150 kJ/mol.

3.

Two Steps and Transitional Model

Several studies have reported a two-stage or transitional process in the rate-controlling step during pyrolysis, leading to models that incorporate both chemical and diffusion control. For instance: Hoare et al. (1988) [53] identified a two-stage mechanism during non-isothermal pyrolysis (Figure 2). The initial stage was chemically controlled, following a three-dimensional shrinking core model (E_a = 286 kJ/mol), while the subsequent stage was diffusion-controlled, consistent with the Ginstling–Brounshtein model (E_a = 190 kJ/mol). Similarly, Lambert et al. (1998) [37] described the process as two consecutive reactions: FeS₂→FeS_X→FeS. The first stage, controlled by S₂ vapor desorption, had an activation energy of 222 kJ/mol; the second stage, controlled by solid-state diffusion of iron, exhibited an apparent E_a of approximately 139 kJ/mol.

It should be noted that the assertion by Pemsler et al. [58] of chemical reaction control, based on the insensitivity of E_a to particle size under He flow, likely misinterprets “mixed control” within chemical control in conventional TGA as intrinsic kinetics.

The compiled data demonstrate that pyrite pyrolysis is characterized by two distinct E_a ranges, each corresponding to a specific rate-controlling step and set of experimental conditions.

As summarized in

Table 2. Pyrite pyrolysis—chemical reaction controlled mechanism (high E_a).

No.	Author	Particle Size	Equipment	Atmosphere	Heating Rate	Model	Ea Value, kJ/mol	Mechanism
1	Hong [25]	2 × 0.05 cm slice	Vertical tube	He, N2, 75 mL/min	Isothermal 400–590 °C	Linear dynamics	297 ± 34	Lattice decomposition
				CO2, 75 mL/min			275± 10	Reacted with CO2
2	Coats [59]	0.25 inches cylinder	Vertical Quartz Tube	Ar 180 mL/min	Isothermal 600–653 °C	McKewan model	270.6–290.7	Chemically controlled
3	Pannetier (as cited from [16,25])		Weight Loss	Vacuum	Isothermal 451–476 °C	Linear kinetics	310
4	Hu [60]	<1 mm	TG-DTG	Dynamic Ar	1000 °C, 2.5, 5, 7.5, 15 K/min	Friedman	268	Lattice defects pyrolysis
5	Concer [61]		TGA	N2 50 mL/min	2.5, 5.0, 7.5, 10.0 K/min.	Friedman	279.2	Volatilization of sulfur
6	Pemsler [58]	70–100, 100–140, 140–200, 270–325 mesh	TG	He 100–250 mL/min	Isothermal 500, 525, 550, 575, 600 °C None-isothermal: 2, 5, 10, 20 °C/min	Shrinking Core Model/First-Order	226–239	Chemical Reaction Control
7	Charpentier [62]	<63 μm	TGA/DSC	Ar 50 mL/min	2–100 °C/min	Firedman	250–350 (average 283 kJ/mol)	Chemical Reaction Control

, a high E_a range (220–310 kJ/mol) characterizes intrinsic chemical reaction control (S–S bond cleavage), which dominates under conditions that ensure efficient S₂ removal.

Conversely,

Table 3. Pyrite pyrolysis—diffusion controlled mechanism (low E_a).

No.	Author	Particle Size	Equipment	Atmosphere	Heating Rate	Model	Ea Value, kJ/mol	Mechanism
8	Lv [63]	63–75 μm	TG	N2, 3000 mL/min	Isothermal 675–800 °C	Shrinking/3D diffusion	103	Step 1: 675–725 °C, Surface desulfurization Step 2: 725–800 °C, Diffusion desulfurization
							93
9	Fegley [27]	slice	High-Temperature Tube	CO2	Isothermal, 390, 416, 468, 500, 530 °C 2.5–7 cm/min	Linear dynamics, Shrinking core	142	Desorption of sulfur
				100 ppm CO-CO2			156
				Ar-CO2			120
				1.1% CO-CO2			153
				CO-CO2-SO2			141
10	Boyabat [64]	0.425–1.4 mm	Tube	N2 1670 cm/min	Non-Isothermal 400–800 °C	Shrinking core	113	Heat transfer at low-temperature Mass transfer at high-temperature
							96
11	Udintsev (as cited from [25])			Vacuum, Ar	Isothermal 400–750 °C	Linear kinetics	110
12	Schwab [65]	0.01–0.1 mm		Air, CO2, H2	400–650 °C	Linear kinetics	125–138
13	Zhukovskii (as cited from [16,25])		Weight Loss	Vacuum, N2	Isothermal 450–690 °C	Linear kinetics	110
14	Samal (as cited from [16,25])		Weight Loss	Vacuum	Isothermal 486–554 °C	Linear kinetics	120

shows that a low E_a range (90–150 kJ/mol) signifies diffusion control, specifically the diffusion of S₂ through the porous Fe_1−XS layer. This mechanism prevails in systems where S₂ accumulates due to rapid pyrolysis with high specific surface area, such as those employing fine powders or low-flow/static atmospheres.

Furthermore, the transitional models in

Table 4. Pyrolysis with two-step or transitional kinetics.

No.	Author	Particle Size	Equipment	Atmosphere	Heating Rate	Model	Ea Value, kJ/mol	Mechanism
15	Jovanović [68]	0.072 mm	thermobalance	N2	Isothermal 600, 660, 700, 750, 800, 850 °C	Farrar-Smith	272	Initially chemical reactions, later diffusion.
						Diffusion control equation	126
16	Hoare [53]	0.58 mg 220 mg particles	Stanton-Redcroft TG761/Cahn RG	N2 35 mL/min and 200 mL/min	3 °C/min non-isothermal	Shrinking core, Ginstling-Brounshtein	286	Step 1: Chemical reaction Step 2: Solid-state diffusion
							190
17	Zhang [51]	0.058 mm	tubular	N2 1 L/min	10 °C/min, 450, 500, 600, 700 °C	Coats-Redfern	199.76	600–700 °C
			Microwave oven		60 °C/min		172.62	500–600 °C
18	Lambert [37]	210 × 250 μm 44 × 53 μm	TGA	Vacuum		Shrinking	222	S2 molecule form
							139	Desorption of S2 molecule
19	Luganov [69]	<0.1 mm	Thermal Analyzer	Ar 8–10 L/min	10 °C/min 20–900 °C	Firedman	193–210	Chemical control at high temperatures Diffusion control at low temperature

demonstrate a shift in the rate-limiting step, confirming that the apparent E_a is a dynamic indicator of the dominant mechanism. Similarly, the kinetics of mineral flotation also demonstrate that the rate-limiting steps undergo dynamic transitions with conditions such as particle size [66,67]. This understanding provides direct kinetic evidence for the competition-coupling mechanism.

The progressive inward advancement of the reaction front during pyrite pyrolysis is physically described by the shrinking core model. The kinetics of this process are mathematically defined by the rate-controlling step: the McKewan model applies to the initial, chemical reaction-controlled stage (high E_a), whereas the Ginstling–Brounshtein model describes the subsequent product layer diffusion-controlled stage (low E_a). For the very early surface reactions, a first-order kinetic equation often provides a valid approximation.

Critically, the dynamic transition between these controlling steps can be captured by the unifying Farrar–Smith model. Regarding kinetic analysis, the Coats–Redfern method is effective only when the correct reaction model is specified. In contrast, the model-free Friedman method directly reveals the continuous evolution of the apparent activation energy (E_a) with conversion. The initial slope method, by isolating the very beginning of the reaction, yields an E_a value closest to that of the intrinsic chemical control.

3.2. Clarifying the Complex Oxidation Mechanisms and E_a

The oxidation behavior is highly sensitive to the local environment and mineral occurrence mode, as evidenced by the significant variations in reported apparent (E_a) and the observed shifts in reaction mechanisms.

3.2.1. Predominant Oxidation Pathways

Synthesizing the extensive literature, the oxidation of FeS₂ can be categorized into four predominant pathways, each with distinct characteristics:

1.

Direct Oxidation to Oxides:

Under low-temperature, high-oxygen conditions, FeS₂ undergoes direct oxidation to Fe₂O₃ or Fe₃O₄ predominantly [16,46,67,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86], often forming a dense oxide shell that can passivate the particle and hinder further oxidation. The apparent E_a for this pathway is typically low (80–120 kJ/mol,

Table 5. Direct oxidation of pyrite to iron oxides.

No.	Author	Particle Size	Equipment	Atmosphere	Heating Rate	Model	Step1 Ea kJ/mol	Step2 Ea kJ/mol	Pathway
1	Hong [25]	2 × 1 × 0.05 cm slice	Vertical tube	O2-CO2, 75 mL/min	Isothermal 400–590 °C	Linear dynamics	392–460 °C 82 ± 52	484–538 °C 293 ± 52	Oxidized layer hinders reaction under 460 °C
				CO2, CO-CO2, 75 mL/min			260–275		Rate constants similar with inert gases
2	Aracena [71,76]	12.3, 16.0, 22.7, 33.8 μm	Vertical tube	O2, 5.07–28.69 kpa,1000 mL/min	Isothermal 550–800 °C	Initial slope	70.1 kJ/mol	/	Temperature accelerates the first stage; Oxygen pressure impacts on second stage

), consistent with a rate-limiting step of oxygen diffusion through the product layer. Studies by McCarty et al. (1989) [77] and Schorr (1969) [83], which observed direct hematite formation without a pyrrhotite intermediate support this mechanism. The formation of a dense product layer is also responsible for a sharp increase in E_a observed under certain conditions.

2.

Indirect Oxidation Via Fe_1−XS:

The sequential transformation of FeS₂→Fe_1−XS→Fe₃O₄/Fe₂O₃ predominates under low-oxygen partial pressures or in larger particles [18,19,22,32,45,71,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114]. In this pathway, pyrolysis precedes oxidation, and the porous intermediate Fe_1−XS layer facilitates inward oxygen diffusion and outward SO₂ release. This exemplifies a classical competition-coupling mechanism between pyrolysis and oxidation.

Pyrolysis and oxidation occur simultaneously in distinct zones within a particle, forming a characteristic “unreacted core-porous intermediate layer-oxide shell” morphology (e.g., Figure 3). The apparent E_a for this route spans a wide range (60–280 kJ/mol, Table 6), reflecting the dynamic balance and potential shift in the rate-determining step between chemical reaction (pyrolysis) and diffusion (oxidation). This mechanism is supported by studies from Dunn et al. (1989) [80], Hansen et al. (2003) [114], Zhou et al. (2018) [113], and Hu et al. (2006) [16], which documented morphology evolution and pathway dependence on O₂ concentration and heating rate.

3.

Sulfate-Mediated Oxidation:

Under S₂-rich atmospheres, FeS₂ forms metastable FeSO₄ or Fe₂(SO₄)₃, which subsequently decompose to Fe₂O₃ at elevated temperatures [9,16,33,52,65,69,71,76,78,79,80,81,97,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131].

This process exhibits a dual E_a signature: a low E_a (~100 kJ/mol) for the exothermic sulfate formation, followed by a high E_a (190–220 kJ/mol) for the endothermic sulfate decomposition (Table 7). The significant volume expansion associated with sulfate formation can passivate the particle, further complicating the kinetics [16].

4.

Molten Phase-Dominated Transformation:

When the transformation temperature exceeds the melting points of iron-sulfur or iron-oxide phases (typically >1083 °C), the mechanism shifts from solid-state processes to melt-dominated kinetics [13,14,18,19,20,94,132,133,134,135,136,137,138,139,140,141]. This transition is characterized by particle spheroidization, accelerated coalescence, and dense sintered deposit formation [132,133,142].

The formation of a low-melting-point FeO-FeS eutectic melt (e.g., ~910 °C) can encapsulate unreacted or partially reacted cores, inhibiting sulfur release and facilitating deposit formation on the matrix. Studies by Huang et al. (2015, 2021) [143,144] and Yu et al. [145] confirm that such molten encapsulation becomes a dominant mechanism at temperatures around 950 °C.

Table 6. Indirect oxidation of pyrite via a porous Fe_1−XS intermediate.

No.	Author	Particle Size	Equipment	Atmosphere	Heating Rate		Model		Step1 Ea kJ/mol	Step2 Ea kJ/mol	Pathway
3	Gomes [146]	7.39 μm	TGA	Air 10 mL/min	2.5–20 °C/min.		Second-order		470–580 °C:145.6 kJ/mol		FeS2 chemical decomposition
					15–20 °C/min.	2.5–7.5 °C/min.	First-order,	Area-contracting	580–1000 °C: 33.2	580–1000 °C: 281.4	Diffusion control in porous	The Fe2O3 layer inhabit reaction
4	Yang [147]		Theoretical calculations				Density Functional Theory (DFT)		197.96/175.83		Surface oxidation Ea of 197.96 kJ/mol, Bulk sulfur migration Ea of 175.83 kJ/mol

Table 6. Indirect oxidation of pyrite via a porous Fe_1−XS intermediate.

No.	Author	Particle Size	Equipment	Atmosphere	Heating Rate		Model		Step1 Ea kJ/mol	Step2 Ea kJ/mol	Pathway
3	Gomes [146]	7.39 μm	TGA	Air 10 mL/min	2.5–20 °C/min.		Second-order		470–580 °C:145.6 kJ/mol		FeS2 chemical decomposition
					15–20 °C/min.	2.5–7.5 °C/min.	First-order,	Area-contracting	580–1000 °C: 33.2	580–1000 °C: 281.4	Diffusion control in porous	The Fe2O3 layer inhabit reaction
4	Yang [147]		Theoretical calculations				Density Functional Theory (DFT)		197.96/175.83		Surface oxidation Ea of 197.96 kJ/mol, Bulk sulfur migration Ea of 175.83 kJ/mol

Table 7. Sulfate-mediated oxidation and decomposition.

No.	Author	Particle Size	Equipment	Atmosphere	Heating Rate	Model	Step1 Ea kJ/mol	Step2 Ea kJ/mol	Pathway
5	Concer [61]		TGA	Air 50 mL/min	2.5, 5.0, 7.5, 10.0 K/min	Friedman	~650 K 924 kJ/mol	~770 K 451 kJ/mol	FeS2→Fe2(SO4)3→Fe2O3
6	Coombs [148,149]	0.1–10 μm	TGA	Air 430 mL/min	648–923 K 10.0 K/min	Friedman	192 kJ/mol	Sulfate decomposition 219 kJ/mol	FeS2→Fe3O4 (low T), FeS2→Fe2(SO4)3→Fe2O3(mid T), and direct Fe2O3 formation (high T).
7	Ferrow [130]	5–40 μm	TGA	Air	200–380 °C	Weibull + Arrhenius	100 kJ/mol		FeS2→FeSO4 below 380 °C. Fe2O3 occurs over 380 °C.
8	Tian [129]	74 μm	TGA	Air 50 mL/min	10 °C/min	Avrami–Erofeev equation Inverse Jander equation	194.81 kJ/mol		FeS2→FeSO4→Fe2O3

The data from Concer (2017) [61] are under questionable due to significant deviation from other existing studies.

Table 7. Sulfate-mediated oxidation and decomposition.

No.	Author	Particle Size	Equipment	Atmosphere	Heating Rate	Model	Step1 Ea kJ/mol	Step2 Ea kJ/mol	Pathway
5	Concer [61]		TGA	Air 50 mL/min	2.5, 5.0, 7.5, 10.0 K/min	Friedman	~650 K 924 kJ/mol	~770 K 451 kJ/mol	FeS2→Fe2(SO4)3→Fe2O3
6	Coombs [148,149]	0.1–10 μm	TGA	Air 430 mL/min	648–923 K 10.0 K/min	Friedman	192 kJ/mol	Sulfate decomposition 219 kJ/mol	FeS2→Fe3O4 (low T), FeS2→Fe2(SO4)3→Fe2O3(mid T), and direct Fe2O3 formation (high T).
7	Ferrow [130]	5–40 μm	TGA	Air	200–380 °C	Weibull + Arrhenius	100 kJ/mol		FeS2→FeSO4 below 380 °C. Fe2O3 occurs over 380 °C.
8	Tian [129]	74 μm	TGA	Air 50 mL/min	10 °C/min	Avrami–Erofeev equation Inverse Jander equation	194.81 kJ/mol		FeS2→FeSO4→Fe2O3

The data from Concer (2017) [61] are under questionable due to significant deviation from other existing studies.

The occurrence mode of pyrite (excluded vs. included) determines the final fate of the iron-containing melt, as shown in Figure 4. For excluded pyrite under reducing conditions, the pathway FeS₂→Fe_1−XS→FeO-FeS eutectic melt is well-established. Under oxidizing conditions, excluded particles can form FeO melt. In contrast, for included pyrite, the resulting Fe-S melt interacts with surrounding aluminosilicates to form FeS and Fe-bearing glass two phases (Figure 5). This indicates that pyrrhotite must first oxidize to FeO before it can be incorporated into the silicate glass phase. This important finding is well documented by McLennan et al. (2000) [28,29].

Under extreme conditions involving very high heating rates and oxygen concentrations (e.g., O₂ ≥ 21%), rapid exothermic oxidation can induce complete particle melting. This results in the formation of spherical droplets with complex surface features (honeycomb-like, tortoise-shell patterns or dendritic) structures as shown in Figure 6, which are predominantly composed of Fe₃O₄ [72]. upon cooling, the formation of a dense Fe₃O₄ shell further passivates the particle. Kinetically, the melting process transitions from solid-state reaction or gas diffusion control to liquid-phase mass transfer.

3.2.2. Kinetic Model of Oxidation

Asaki et al. (1989, 1985) [138,139] were the first to propose an oxidation model for Fe_1−XS particles in a vertical tube reactor, applying shrinking core model that integrated mass transfer, heat transfer, and interfacial reaction kinetics. Their model assumed that Fe_1−XS oxidizes to solid Fe₃O₄ below 1468 K but melts at 1468 K. The simulations demonstrated that melting commenced between 950 and 1200 K at pO₂ > 2.02 × 10⁴ Pa, driven by exothermic reaction heat elevating the temperature beyond its melting point. The model also indicated that while smaller particles (e.g., 51 μm) initially oxidized faster than 88 μm particles due to their larger specific surface area, they may experience delayed further oxidation from earlier formation of denser oxide layers. A key limitation of this model is its presumption of an indirect oxidation pathway from pyrrhotite (Fe_1−XS) to magnetite (Fe₃O₄), which fails to describe the formation of sulfate intermediates and their significant impact on reaction kinetics. Srinivasachar et al. (1989) [23] developed an alternative kinetic model base on thermal and mass balance equations, which suggest that the particles spend approximately 80% of the total transformation time in a molten state. Building on this work, Jassim et al. (2011) [141] improved the model by incorporating particle fragmentation, with simulations demonstrating that fragmentation shortens the heating time required to reach the melting point.

3.2.3. Synthesis of Oxidation Activation Energy

The complex and variable pathways of FeS₂ oxidation have limited studies on its activation energy, as summarized in Table 5, Table 6 and Table 7.

The sudden shift in E_a from 82 kJ/mol to 293 kJ/mol around 460 °C in O₂-CO₂ observed by Hong et al. (1997) [25] is not only a temperature effect but results from a morphological transition in the product layer: a porous layer at low temperature allows for rapid diffusion (low E_a), while a dense layer at high temperatures impedes oxygen diffusion, raising the apparent E_a to near-pyrolysis levels.

Gomes et al. (2022) [146] found that during the late oxidation stage (580–1000 °C), the apparent E_a divided into two values (~33.2 kJ/mol and ~281.4 kJ/mol) depending on the heating rate, revealing two competing mechanisms: rapid heating maintains a porous structure, leading to reaction control (low E_a), whereas slow heating causes product layer densification, shifting the control to diffusion through the layer (high E_a). This study thus confirms that no single “oxidation mechanism” exists, as the apparent E_a is highly dependent on the intermediate phase microstructure dictated by the thermal history.

Notably, the implausibly high activation energy of 924 kJ/mol reported by Concer et al. [60] for the oxidation cannot represent an intrinsic kinetic barrier but rather signals severe diffusion limitations from layer passivation.

Table 5 shows that direct oxidation to oxides, governed by oxygen diffusion, is characterized by low E_a values (80–120 kJ/mol). In contrast, the indirect route via a Fe_1−XS intermediate (Table 6) exhibits a wide E_a range (60–280 kJ/mol), reflecting the dynamic balance between pyrolysis and oxidation. Table 7 further highlights the dual role of sulfates, with low E_a formation and high E_a decomposition.

This pathway classification, however, does not fully capture the dynamic nature of the oxidation process. Vázquez et al. (2019) [150] observed a progressive decrease in E_a from ~450 kJ/mol to ~80 kJ/mol during a single oxidation process, indicating a clear shift in the rate-determining step. Similarly, Charpentier et al. (2010) [62] demonstrated the E_a value for pyrite pyrolysis varies with the reaction progress. Together, these observations demonstrate that the apparent E_a is not a fixed value but a dynamic indicator.

Kinetic models for pyrite oxidation are highly diverse, ranging from geometrical contraction models (surface chemical control) to Jander-type models (product layer diffusion control), reflecting the complexity and multi-mechanistic nature of the process. Furthermore, semi-empirical approaches like the Weibull + Arrhenius model are particularly suited for such complex systems with parallel pathways, as they characterize the distribution of reaction conversion and then determine the corresponding activation energy.

3.3. Evidence for the Interplay Between Pyrolysis and Oxidation Kinetics

To synthesize the extensive kinetic data from Section 3.1 and Section 3.2.3, Figure 7 illustrates the continuous variation in reported E_a for both pyrolysis and oxidation processes.

As shown in Figure 7, the E_a values are distributed across distinct intervals. Pyrolysis-dominated reactions exhibit activation energies of 220–310 kJ/mol (corresponding to S–S bond cleavage) and 90–150 kJ/mol (corresponding to S₂ vapor diffusion). In contrast, direct oxidation-dominated reactions, governed by oxygen diffusion kinetics, have lower activation energy values (80–120 kJ/mol). However, indirect oxidation exhibits the broadest ranges (60 to 280 kJ/mol), where pyrolysis and oxidation occur simultaneously.

The empirical trend line in Figure 7 qualitatively maps the evolution of the apparent activation energy (E_a). More importantly, broad, continuous distribution of E_a values is a characteristic kinetic signature of the competition-coupling mechanism, in which E_a measured at any point represents the dynamic balance. The approach of resolving complex transformations into distinct mechanistic zones is consistent with previous studies that found that the dominant flotation mechanism shifts with particle size changes and energy input [66,151]. Consequently, this mechanism reconciled the discrepancy among E_a values reported in the literature.

4. Proposing the Competition-Coupling Mechanism and Constructing the Unified Phase Diagram

4.1. The Principle of Competition-Coupling Mechanism

Competition arises from intrinsic gradients of oxygen partial pressure and temperature within a particle. The surface, which is directly exposed to the bulk gas, constitutes an oxidation-dominated zone. In contrast, the particle core, where oxygen is depleted by the surface reaction and inward diffusion is hindered, becomes a pyrolysis-dominated zone.

Coupling occurs in two key stages:

• Pyrolysis couples forward to oxidation: The initial pyrolysis of FeS₂ generates a porous Fe_1−XS intermediate, creating a “core-pore” structure. This porosity enhances the inward diffusion of oxygen, thereby facilitating the subsequent oxidation of the intermediate.
• Oxidation couples backward to pyrolysis: The oxidation of Fe_1−XS can lead to the formation of a dense oxide or sulfate shell, resulting in a “core-pore-shell” morphology. This shell limits oxygen access to the core, which in turn promotes the continuation of pyrolysis internally.

4.2. A Predictive Phase Diagram: Bridging Thermodynamics and Kinetics

Although Figure 1 offers a thermodynamic “map” of equilibrium possibilities, the actual transformation is governed by dominant reaction mechanisms under non-equilibrium conditions. To address this divergence, we propose a theoretical phase diagram (Figure 8) that incorporates competition-coupling mechanism. This diagram is categorized into four distinct transformation regions.

1.

Pyrolysis-Dominated Region

Location: High molar ratio regime where FeS₂/(FeS₂ + O₂) ≈ 60%–100%, typically between 563 °C and 947 °C, or under fully inert conditions.

Kinetic Mechanism and Signature: This region is characterized by the endothermic pyrolysis of FeS₂. The kinetics exhibit high apparent activation energies (220–310 kJ/mol) corresponding to the cleavage of S-S bonds in the initial stage (FeS₂→Fe_1−XS + S₂). Morphologically, the reaction produces a characteristic “unreacted core-porous shell” structure.

Final Products: Troilite (FeS) is the primary product, which may form a molten phase above ~947 °C (or ~1180 °C if silicate interactions occur).

2.

Competition-Coupling Region

Location: This region covers a broad domain defined by three primary conditions: high molar ratio regime (FeS₂/(FeS₂ + O₂) ≈ 100%–60%) at temperatures below 563 °C, intermediate molar ratio regime (FeS₂/(FeS₂ + O₂) ≈ 60%–47.1%) at temperatures below 1069 °C, and low molar ratio regime (FeS₂/(FeS₂ + O₂) ≈ 47.1%–28.6%) at temperatures ranging from 480 °C to 1069 °C.

Kinetic Mechanism and Signature: This is the most complex region, where pyrolysis and oxidation reactions compete and couple dynamically. The mechanism typically involves two pyrolysis stages generating a porous Fe_1−XS intermediate. This enhanced porosity facilitates inward oxygen diffusion for further oxidation to Fe₂O_3, Fe₃O₄, and even sulfate. This coupling results in a multi-layered “unreacted core-porous layer-shell” morphology (e.g., FeS₂ core/Fe_1−XS layer/Fe₃O₄ or Fe₂O₃ or sulfate shell). Consequently, the apparent E_a in this region is not fixed [66] but forms a continuous curve (Figure 7).

3.

Oxidation-Dominated Region

Location: Low molar ratio regime where FeS₂/(FeS₂ + O₂) ≈ 28.6%–0%, and regime where FeS₂/(FeS₂ + O₂) ≈ 47.1%–28.6% is below 480 °C.

Kinetic Mechanism and Signature: The transformation is dominated by direct exothermic oxidation, characterized by lower apparent activation energies (80–120 kJ/mol) typical of diffusion of oxygen through a product layer. At lower temperatures, sulfates (FeSO₄ and Fe₂(SO₄)₃) form as metastable intermediates, leading to initial mass gain and particle passivation with E_a ≈ 100 kJ/mol. The subsequent decomposition of these sulfates has a higher E_a (190–220 kJ/mol). Morphologically, dense oxide/sulfate shells often form, which can hinder further reaction progress. Critically, the formation of such dense shells can shift the dominant mechanism from direct to indirect oxidation, resulting in a sharp increase in the apparent E_a.

4.

Melt-Dominated Region

Location: High-temperature domain across all molar ratio regimes.

Kinetic Mechanism and Signature: At elevated temperatures, solid products melt, shifting the transformation mechanism from solid-state reaction/diffusion to liquid phase mass transfer. Morphologically, particles start to spheroidize, which possibly leads to the formation of dense deposits upon cooling. The melting temperature is system-dependent: for example, it is ~947 °C for FeS, ~1180 °C for FeS-FeO, and 1069 °C for Fe₃O₄ under oxygen-lean and moderate-oxygen regimes, and ~1565 °C for Fe₃O₄ in an oxygen-rich regime.

Unlike conventional thermodynamic diagrams that describe equilibrium states (“what should happen”), our diagram’s key innovation is its ability to predict feasible pathways under non-equilibrium conditions (“what can happen”). It achieves this by incorporating competition-coupling mechanisms into its thermodynamic framework, thereby bridging the gap between thermodynamic prediction and kinetic reality.

4.3. Practical Modulators: Particle Size, Heating Rate, and Occurrence Mode

Additionally, practical combustion involves critical factors that indirectly modulate temperature and atmospheric composition.

1.

Particle Fragmentation Effects:

FeS₂ pyrolysis releases sulfurous gases, generating internal pressure. When this pressure exceeds the yield strength at FeS₂/Fe_1−XS interfaces, it causes particle fragmentation. This process critically enhances oxidation accessibility [152], shifting the competitive balance toward oxidation.

Boyabat et al. (2004) [64] confirmed enhanced pyrolysis rates with decreasing particle size, while Srinivasachar et al. (1989) [23] established that FeS₂ oxidation time is proportional to d² (53–75 μm particles exhibit >30% slower S-release than 38–45 μm particles). Hu et al. (2006) [16] observed that fine particles (<0.045 mm) undergo direct oxidation to Fe₂O₃, whereas coarser fractions (0.09–0.12 mm) favor a sequential decomposition-oxidation pathway. This phenomenon, where particle size governs the reaction pathway, has also been observed in the kinetics of coal slime flotation [66,153]. Hawkins et al. (2014) [154], Baxter et al. (1992) [155,156], and Elder et al. (1965) [106] attributed accelerated oxidation to increased reactive surface area, surface roughness, and microcracking resulting from fragmentation.

In summary, fragmentation is a critical positive feedback mechanism that promotes oxidation by drastically improving O₂ accessibility.

2.

Heating Rate Dependence:

Slow heating facilitates direct FeS₂ oxidation but also leads to the formation of a sulfate/Fe₂O₃ layer that inhibits reactions. Conversely, rapid heating suppresses direct oxidation, allowing pyrolysis to occur preferentially. As demonstrated by Yani et al. (2010) [157], complete decomposition is achieved by 1200 K at 10 K/min, but remains incomplete even at 1250 K when heating rate is increased to 50 K/min.

Furthermore, high heating rates and large particle sizes yield underestimated E_a values due to internal temperature gradients, while isothermal or slow-heating conditions provide closer estimations of intrinsic E_a.

3.

Excluded vs. Included FeS₂:

Excluded particles: Direct exposure enables rapid oxidation [158,159].

Included particles: Coke-derived reducing environments delay oxidation [87,160]. When in contact with aluminosilicates, it forms FeS/Fe-glass biphasic particles. Crucially, full incorporation of FeS into the glass phase requires its oxidation to FeO first. This pathway is consistent with the work of Zhao et al. (2015) [161] and Bool et al. (1995) (1996) [21,22], who summarized the distinct route as follows: Excluded FeS₂→Fe_1−XS→molten Fe-O-S→Fe₃O₄. Included FeS₂→Fe_1−XS→silicate-glass phase.

4.4. Validation: Mapping Pathways in the Literature onto the Phase Diagram

An attempt to validate the proposed unified phase diagram encountered a fundamental challenge: oxygen concentrations reported in the literature are typically given as volume percentages, which are influenced by gas flow rates, reactor geometry, and pressure. These values are not convertible to the molar ratio FeS₂/(FeS₂ + O₂) used herein. Despite this limitation, the dominant transformation pathways identified in previous studies were systematically mapped onto the phase diagram in Figure 9.

1.

Direct and Sulfate-Mediated Oxidation (red arrowed line in the diagram):

FeS₂→Fe₂O₃: (3) Bhargava [102], (20) Hu [16], (23) Jorgensen [17], and (33) Almeida [119].

FeS₂→FeSO₄ or Fe₂(SO₄)₃→Fe₂O₃: (1) M.Vázquez [150], (12) Earnest [78], (13) Thomas [118], (14) Komraus [162], (33) Almeida [119].

FeS₂→FeSO₄→Fe₂O₃: (17) Ferrow [130,131], (37) Concer [61].

FeS₂→FeSO₄→Fe₂(SO₄)₃→Fe₃O₄: (17) Ferrow, (39) Banerjee [120].

2.

Pyrrhotite (Fe_1−XS)-Mediated Pathways (green arrowed line in the diagram):

FeS₂→Fe_1−XS→FeSO₄→Fe₂(SO₄)₃→Fe₂O₃: (1) M.Vázquez [150], (9) Paulik [122], (13) Thomas [118], (15) Zhang [35], (32) Coombs [148], (37) Concer [61], (39) Banerjee [120].

FeS₂→Fe_1−XS→Fe₂O₃: (11) Music [46].

FeS₂→Fe_1−XS→Fe₃O₄→Fe₂(SO₄)₃ or FeSO₄→Fe₂O₃: (23) Jorgensen [17], (25) PeterHansen [114].

FeS₂→Fe_1−XS(→Fe₃O₄)→Fe₂O₃: (2) Hong [25] and Fegely [27], (10) Thrope, (19) Aracena [71,76], (20) Hu [16], (21) Bool [21,22], (27) Liu [73,74,163], (41) Schoenlaub [97].

FeS₂→Fe_1−XS→Fe₃O₄ and Fe_1−XS→Fe₂O₃: (4) Wang [103], (18) Tomeczek, (28) Wang [72,164], (30) McLennan [28], (31) Tao [165], (36) Yu [112], (38) Wang [98].

FeS₂→Fe_1−XS→Fe₃O₄→melt→Fe₃O₄→Fe₂O₃: (24) Jassim [141].

3.

Melt-Involving Pathways (blue arrowed line in the diagram):

FeS₂→Fe_1−XS→Fe₃O₄ (or Fe₂O₃)→melt: (22) Asaki [138,139], (26) Sheng [159], (28) Wang [72,164], (29) Huffman [18,19,94], (34) Helbe [93], (35) Huffman [19], (36) Yu [112].

FeS₂→Fe_1−XS→melt: (6) Huang [143,144].

FeS₂→Fe_1−XS→FeS + FeO: (5) McLennan [29].

FeS₂→Fe_1−XS→FeS + FeO→Fe₃O₄→Fe₂O₃: (16) Srinivasachar [23].

4.

Other Pathways (yellow arrowed line in the diagram):

FeS₂→Fe₃O₄→Fe_1−XS: (8) Li [88].

FeS₂→Fe_1−XS→Fe₃O₄: (3) Bhargava [102], (7) Wu [30,32].

The successful mapping of 16 distinct literature-derived pathways onto the four regions of our phase diagram (Figure 9) validates the framework’s consistency and predictive power. Previously anomalous pathways, such as (8) Li [88], (3) Bhargava [102], and (7) Wu [30,32], are logically explained within the competition-coupling region. This reinterpretation of disparate pathways emphasizes the validity of the proposed diagram and its advantage over intertwined pathways.

5. Conclusions and Future Perspectives

5.1. Key Findings and Conclusions

This work establishes a unified framework for pyrite thermal transformation, with the following key findings:

1.

Proposal of the Competition-Coupling Mechanism:

We proposed a novel competition-coupling mechanism wherein pyrolysis and oxidation compete under local O₂ and temperature gradients, while simultaneously coupling through microstructural evolution. Specifically, pyrolysis generates a porous Fe_1−XS intermediate that facilitates oxidation, which in turn forms a passivating layer that promotes further pyrolysis.

2.

Reconciliation of Kinetic Data: E_a as a Dynamic Signature of Mixed Reaction.

The apparent E_a is identified as an indicator of the rate-determining step. It varies continuously from pyrolysis-dominated regimes (high E_a for S–S bond cleavage) to oxidation-dominated regimes (low E_a for O₂ diffusion). This principle provides a unifying interpretation for reconciling disparate kinetic data in the literature.

3.

Construction of Phase Diagram: Bridging Theory and Practice.

We constructed an original, unified phase diagram that categorizes the transformation process into four distinct regions—pyrolysis-dominated, competition-coupling, oxidation-dominated, and melt-dominated—based on the molar ratio FeS₂/(FeS₂ + O₂) and temperature. This kinetically modified diagram predicts feasible pathways under non-equilibrium conditions.

This framework provides a fundamental understanding for controlling sulfur emissions and mitigating ash-related issues (e.g., slagging and fouling) in coal combustion, roasting, and gasification processes, thereby contributing to the advancement of clean coal utilization technologies.

5.2. Future Challenges and Research Directions

The proposed framework highlights several key challenges for future work:

• Quantifying Kinetic Phase Boundaries: Future research should employ techniques like HT-SEM, HT-XRD, and in situ XPS to quantitatively map how boundaries shift with particle size, heating rate, and gas flow, ultimately enabling the construction of a precise predictive diagram.
• Defining the Role of Sulfates: The critical switch between sulfate present as a temporary transitional intermediate or a final passivating layer requires clarification through surface analysis (XPS) and coupled TG-MS.
• Quantifying the Competition-Coupling Mechanism: Advanced kinetic analysis is required to distinguish whether pyrolysis and oxidation reactions are independent or strongly coupled.

5.3. Theoretical Limitations

The proposed framework is subject to the following constraints:

• Pathways, Not End States: The phase diagram predicts the dominant kinetic pathway, rather than the final thermodynamic equilibrium. This explains why pyrolysis can prevail over thermodynamically favored oxidation in realistic.
• Apparent E_a as a Composite Metric: In the competition-coupling region, the apparent activation energy represents a blend of overlapping processes. It reflects the dynamic balance between pyrolysis and oxidation rather than a single elementary step.
• Static Situation Assumption: The phase diagram does not account for dynamic flow or particle fragmentation, which can instantaneously expose fresh surfaces and drastically alter the transformation pathway.