Sintering and thermokinetic modeling of the phase evolution in thermite powder mixtures under controlled heating

Introduction

The in-situ formation of strengthening particles in metal–matrix composites (MMCs) has become a focal point in powder-processing technologies owing to applications across the aerospace, automotive, and energy sectors, and it continues to attract sustained interest from diverse research groups [1–4]. The spectrum of MMCs obtainable by powder routes is broad – in terms of both matrix chemistries and sets of strengthening phases. Of particular interest are systems built from chemically reactive powder components, where reactions between constituents synthesize the strengthening phases in-situ as micron-scale inclusions. This is largely characteristic of combustion-synthesis routes that rely on metallothermic reactions [5–9]. Such reactions are typically strongly exothermic, which helps sustain the synthesis process. Creating the strengthening particles directly during composite fabrication is advantageous for interfacial bonding with the surrounding matrix. However, when a mixture permits metallothermic reduction (one metal reducing another), the presence of additional constituents can markedly redirect reaction pathways because local interaction conditions vary across different regions of the compact [10].

The problem becomes even less straightforward if one component of the powder mixture is itself a complex material – namely, a metallic base containing oxide inclusions – produced by recycling steel chips [11].

Here, the feasibility of producing metal–matrix composites from Al–Fe₂O₃–Fe and Ti–Fe₂O₃–Fe powder mixtures (optionally containing carbon) under sintering in a vacuum chamber is assessed, together with a theoretical description based on a thermokinetic model that accounts for the kinetics of the principal reactions.

1. Experimental

1.1. Materials and methods

Phase evolution under vacuum sintering with a controlled heating program (sintering temperature 1173–1473 K; 60-min hold) was examined for powder systems based on Ti–Al–Fe₂O₃/(Fe + C) using the following representative mixtures (from several possible combinations): Al + (Fe + Fe₂O₃ + C) and Ti + (Fe + Fe₂O₃ + C). Titanium powder TPP-8 (main fraction d < 160 μm) and aluminum powder PA-4 (d < 100 μm) were used to prepare the mixtures. As an analogue of the Fe + Fe₂O₃ + C composition, a powder produced from recycled steel 45 chips with a particle size not exceeding 300 μm was employed; its characteristics are described in detail in [11]. The component ratios in the mixtures were calculated to be sufficient both for metallothermic reduction and for intermetallic formation. The quantitative compositions of the powder mixtures under study are given in Table 1.

Selection of proportions for the aluminum-containing mixtures was guided by the binary Al–Fe phase diagram. The first option corresponds to the α-AlFe₃ field, while the second lies predominantly in the Al₃Fe/AlFe phase region. Both options imply exothermic reactions.

The titanium-containing mixture comprised 75 wt. % Ti and 25 wt. % steel chips, which favors the formation of a matrix basis in the resulting composite as a solid solution of iron and oxygen in titanium.

Microstructural characterization was performed by optical microscopy, scanning electron microscopy (SEM), and X-ray diffraction (XRD). The following instruments were used: Axiovert 200MAT optical microscope (Carl Zeiss, Germany), Mira 3 LMU SEM (Tescan, Czech Republic), and XRD-600 (Shimadzu, Japan) and DRON-8 (Russia) diffractometers with CuK_α radiation. Phase identification employed the PDF-4+ database and POWDER CELL 2.4 for full-profile analysis.

According to [11], chips oxidized in water and then milled form oxide-coated steel-chip fragments with an Fe core, containing dissolved carbon (≈1.5 wt. %). Although carbide phases were not detected by XRD, the presence of carbon in the steel-chip particles was confirmed by energy-dispersive X-ray spectroscopy (EDS). Carbon content, measured with a LECO ONH-836 gas-impurity analyzer (USA), showed a broad distribution (0.8–1.6 wt. %), reflecting the substantial heterogeneity of the processed steel-chip–derived particles. Their surfaces bear iron-oxide regions (Fe₃O₄/Fe₂O₃/FeO) [11], with the oxide fraction reaching ≈50–70 %. Because these oxide layers are highly nonuniform (Fig. 1), the contact between a chip-derived particle and Al or Ti powder depends on the local surface domain encountered. Within the same mixture, the second component can therefore contact metallic iron (carbon steel) and iron oxides simultaneously.

1.2. Experimental results

Under vacuum sintering at T_s = 1273 K, a heterogeneous phase assemblage was identified for both Al + (Fe + Fe₂O₃ + C) formulations [12]. The pressed compacts of aluminum powder with milled, oxidized steel chips lost structural integrity and disintegrated into separate fragments. The selected sintering conditions were sufficient to initiate a cascade of reactions, yielding Fe–Al intermetallics together with oxide strengthening particles. Residual (unreacted) iron was also detected in the products (Fig. 2). Oxygen was transferred almost entirely from the iron oxides to aluminum, forming Al₂O₃, and FeAl constituted the dominant volumetric fraction of the product.

With increasing aluminum content in the compact, the reaction products contained a substantial fraction of residual, unreacted constituents, attributable to a decrease in the overall exothermicity of the reactions.

The second formulation, Ti + (Fe + Fe₂O₃ + С), is less exothermic. Since the solubility of iron in β-Ti reaches 22 at. % at T_s = 1358 K and drops to 0.34 at. % in α-Ti at 673 K, it was expected that part of the iron would react with titanium to form intermetallics. It was also anticipated that titanium would be sufficient to interact with oxide inclusions present in the recycled steel-chip powder. Experimentally, the steel-chip powder in the Ti + (Fe + Fe₂O₃ + C) mixture exhibited good sinterability, with predominantly diffusional interaction with iron and oxygen migration from iron oxides into the titanium matrix. It is plausible that carbon contained in the chips enhances sintering via diffusion into titanium; however, its amount is too low to produce titanium carbide at levels detectable by X-ray diffraction. Interaction of free iron with titanium in the presence of oxide inclusions does not impede interdiffusion. The phase set and phase fractions depend on the sintering temperature; nevertheless, in all cases the products are dominated by a titanium-based solid solution (Fig. 3). At lower temperatures, the products contain a nonstoichiometric TiO₂-based oxide (18 wt. %) and residual Fe₂O₃ (32 wt. %) originating from the steel-chip particles. Iron from these particles reacts with titanium to yield up to 20 wt. % of the equiatomic intermetallic TiFe. At a higher sintering temperature (1473 K), no unreacted constituents remain, and two types of α-Ti–based solid solutions form with different dissolved Fe and O contents; small inclusions of Ti₂Fe, TiFe₂, or TiFe are also observed. Oxides are not detected as a separate phase under these conditions (Fig. 3).

The results reported in [13; 14] provided the basis for constructing thermokinetic models that capture the staged nature of phase formation.

2. Sintering model with detailed kinetics

2.1. Heat balance

The thermokinetic model accounts for the sample temperature change arising from the controlled external heating program and from heat release by chemical reactions. Owing to the small sample size, temperature gradients within the compact are neglected (a lumped-capacitance assumption); estimates justifying this approximation are given in [15]. The heat-balance equation has the form

where T is the temperature; t is time; V and S are the compact volume and surface area; с and ρ are the heat capacity and density of the pressed powder mixture; W_ch is the total heat release due to chemical reactions; σ is the Stefan–Boltzmann constant; ε is the surface emissivity of the compact; α is the heat-transfer coefficient (in vacuum it may be taken as zero); Т_е is the ambient temperature (if Newton cooling is included).

The vacuum-chamber wall temperature T_W follows a linear law:

where а is the heating rate and T_s is the sintering temperature.

Within the interval T_min–T_max , melting is assumed to occur, with the liquid-phase fraction (η_L) varying from 0 to 1:

Here, T_min is the lowest melting temperature among the reagents and reaction products in the chosen system, and T_max is the highest one (see Table 2).

Within the melting interval, the (specific) heat capacity is given by

where с_S is the heat capacity of the mixture in the solid state, c_L is the heat capacity of the mixture in the liquid state; Q_eff is the effective enthalpy of fusion (J/mol); m is the mean molar mass of the mixture of reagents and reaction products.

Heat release from chemical reactions is given by

where n is the number of reactions; Φ_i are the reaction rates; Q_i are the reaction enthalpies (heat effects).

2.2. Model of phase composition
evolution during sintering

Because the detailed mechanisms of most solid-state reactions are rarely known and the steps involved often comprise a mix of physicochemical processes, it is most appropriate to use a reduced-chemistry model that explicitly tracks the formation of the experimentally observed phases.

In the Al-containing system (where aluminum has the lowest melting temperature), the dominant exothermic step is expected to be the aluminothermic reduction of iron oxide:

The reduced iron then reacts with excess aluminum to form intermetallic phases. Owing to the large reaction enthalpies, phase formation is expected to occur predominantly in the liquid phase and to be accompanied by the appearance of agglomerates [16]. At the same time, as noted in [17], direct reaction between aluminum and iron oxides during combustion is preceded by the partial decomposition sequence Fe₂O₃ → Fe₃O₄ → FeO. Thin plates of FeAl₂O₄, have been observed in [17] as a result of the interaction between FeO and the amorphous Al₂O₃ film that invariably coats aluminum:

Iron aluminates such as FeAl₂O and FeAl₂O₄ commonly appear in the Al–Fe₂O₃ system, which is unfavorable for further reduction of iron oxides – especially in the presence of Al₂O₃ [18].

In the Al–Fe₂O₃ system, an additional step may occur

followed by oxidation of aluminum:

The Al–Fe phase diagram contains several intermetallic phases (Fig. 4). The diagram was constructed using the Thermo-Calc Software (open version) with the TCBIN: TC Binary Solutions v1.1 database.

Formation of intermetallic phases proceeds via the reactions

The FeAl intermetallic is not shown on the diagram; however, it is known to form by ordering of the α-Fe(Al) solid solution. Fe₃Al is a metastable phase that appears via a second-order phase transformation from FeAl [19]. Carbon present in the processed chips could, in principle, participate in the synthesis of aluminum carbide (Al₄C₃), but the sintering schedule and mixture composition do not provide sufficient carbon or temperature to initiate the corresponding reaction.

In the second case (Ti–Fe₂O₃–Fe–C system), iron is the lowest-melting component (see Table 2). According to [20], the thermite reaction Ti–Fe₂O₃ proceeds through several steps – reduction of Fe₂O₃ by Ti to form Fe and TiO₂, followed by the formation of the metastable intermetallic Ti₂Fe. Allowing for partial decomposition of iron oxide, the presence of carbon, and the formation of intermetallic phases (Fig. 4, b), the reaction set can be written as:

The notation for species concentrations (С_k) for each system is given in Tables 3 and 4.

For each reaction network, the kinetic equations can be written as

where ν_ki are the stoichiometric coefficients of component k in reaction i; r is the number of reactions, Ф_i are the reaction rates. We assume that the reaction rates follow an Arrhenius temperature dependence and depend on concentrations according to the law of mass action:

Here, n_ki are the exponents equal in absolute value to the corresponding stoichiometric coefficients;

where k_i0 are the pre-exponential factors; E_i are the activation energies; R is the universal gas constant. The rate expressions for all reactions are given in Table 5.

Thus, for the first system we require 27 formal kinetic parameters k_i0, E_i, Q_i, and for the second – 24. Using published parameters for overall reactions in SHS-type mixtures [21] is not feasible. One reason is the strong dependence of parameters on the determination method, mixture processing, heating rate, etc. Another is the lack of data for most steps. Even for one of the most studied thermite mixtures (Al–Fe₂O₃), published values are inconsistent [22], including the reaction enthalpies. For example, for reaction (VI) in the Al-containing system, [23] gives: ΔH = –851.4 kJ/mol, whereas [16] reports ΔH ≈ –752 kJ/mol.

The entropies and enthalpies of reactions were obtained using Hess’s law:

where the first terms on the right-hand side are sums of the parameters for the reaction products, and the second terms are the parameters for the reactants (reagents in the formula). However, tabulated values are not available in the literature for all compounds. For this reason, approximate semi-empirical methods were used to obtain preliminary estimates of the formal kinetic parameters (Table 6). The parameter-estimation procedure is described in detail in [15].

For each system, the problem (which comprised 10 and 9 ordinary differential equations of the form (6) for the Al- and Ti-containing systems, respectively, plus the heat-balance equation (1)) was solved numerically using a semi-implicit Euler method. In every run, mass conservation and atomic balance were verified. Calculations were performed at constant \(\Delta S_{298}^0\) and \(\Delta H_{298}^0\). The reaction orders were adjusted during the numerical solution. For the first system, we obtained:

k₀₁ = 10¹⁷, k₀₂ = 10²², k₀₃ = 3·10²², k₀₄ = 10²²,
k₀₅ = 10²², k₀₆ = 8·10¹⁹, k₀₇ = 6·10¹⁵,
k₀₈ = 10¹⁵, k₀₉ = 10²⁴ s^–1.

For the second system, the adjustments affected two pre-exponential factors and the activation energy of one reaction:

k₀₅ = 3·10¹⁹ s^–1, k₀₆ = 6·10²³ s^–1,
E₆ = 150 255 J/mol.

A single scaling factor applied to all reactions was 10^–17 for the Al-containing system and 7.5·10^–13 for the Ti-containing system. The criterion for selecting this factor was the characteristic reaction time under the experimental conditions.

2.3. Numerical analysis results

Calculated temperature and composition profiles for reactive sintering of the studied systems are shown in Figs. 5–7. The typical temperature curves differ for the Al- and Ti-containing mixtures (Fig. 5). In the former, a temperature spike appears upon reaction initiation at Т = 700–900 K. In the latter, there is no pronounced spike, although a wavy temperature curve is observed.

Such behavior is often ascribed to thermocouple sensitivity; however, the calculations indicate that it may also arise from the interplay of coupled physicochemical processes.

As noted above, the exact oxide composition in the chips is unknown. Accordingly, the modeling allows for different choices of initial data (Table 7). We assume the presence of two iron oxides – FeO and Fe₂O₃. Fe₃O₄ can, to first approximation, be treated as a combination of FeO and Fe₂O₃ and is therefore not included explicitly. In addition, the numerical experiment accounts for adsorbed oxygen and alumina on particle surfaces. Only under this assumption does the model reproduce the amount of Al₂O₃ observed experimentally in the products. The numerical study further enables exploration over a wide range of initial compositions, which is difficult to achieve experimentally.

No such complications arose for the Ti system, although the initial composition of the powder mixture can likewise be varied numerically.

Composition-evolution results for different initial data are presented in Figs. 6 and 7. We find that the product composition can vary substantially. For the Al-containing system (Fig. 6), the products always contain Fe₃Al and FeAl₃ intermetallics in different proportions, as well as Al₂O₃. The reduction of iron is the fastest reaction. FeAl is not observed in the products. The mixed oxide appears only when the initial mixture contains Al₂O₃, FeO, and oxygen; in that case, Fe₂Al₅ is also present. The experimental data are best matched by Composition 2, which includes oxygen and oxide in the starting mixture.

The phase composition of the Ti compact also evolves (Fig. 7). All reactions proceed actively over a time interval shorter than the total sintering time. For all initial compositions, the products always contain the intermetallic Ti₂Fe and unreacted Ti. TiFe appears as an intermediate during sintering. In three variants, the product contains Ti₃FeO₂. In the second variant, the starting mixture contains a small amount of iron oxide, hence its role is minor; however, Fe₂O₃ most closely reflects the experimental conditions. Under the experimental conditions, the product contains 91 wt. % of α-Ti solid solution + Ti₂Fe and α-Ti solid solution + TiFe. In this case, Fe₂O₃ is insufficient to form TiO₂. In the other three variants, TiO₂ appears as an intermediate that is consumed rapidly to form the complex oxide.

Conclusion

This study demonstrates good agreement between the proposed thermokinetic model and experimental data for multicomponent powder mixtures – recycled steel-chip powder with aluminum or titanium – under vacuum sintering. Consistent with the experiments, the calculations predict substantial heat release upon heating Al + (Fe + Fe₂O₃ + C) mixtures, whereas Ti + (Fe + Fe₂O₃ + C) sinters in a steady regime. In the former case, aluminum carbide was not included in the model because of the low sintering temperature; in the latter, titanium carbide formed only in trace amounts. No carbides were detected experimentally in either system.