# Effect of Particle Size and Magnesium Doping on Fe/CuO Pyrotechnic Composition Combustion

Nabil Mokrani, Davney Ondzié-Pandzou, Stéphane Bernard, Jean-Claude

Harge, Léo Courty

► To cite this version:

Nabil Mokrani, Davney Ondzié-Pandzou, Stéphane Bernard, Jean-Claude Harge, Léo Courty. Effect of Particle Size and Magnesium Doping on Fe/CuO Pyrotechnic Composition Combustion. Fuel, 2026, 418 (138666), pp.138666. 10.1016/j.fuel.2026.138666. hal-05504615

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Full Length Article

# Effect of Particle Size and Magnesium Doping on Fe/CuO Pyrotechnic Composition Combustion

Nabil Mokrani<sup>a</sup>, Davney Ondzié-Pandzou<sup>a</sup>, Stéphane Bernard<sup>a</sup>, Jean-Claude Harge<sup>b</sup>, Léo Courty<sup>a,*</sup>

## ARTICLE INFO

Keywords:

Energetic materials

Pyrotechnic compositions

Burning rate

Iron

Copper oxide

## ABSTRACT

This study explores the combustion behavior of Fe/CuO thermite systems by systematically evaluating the effects of iron particle size, Fe content, porosity, and magnesium (Mg) doping. Thermite pellets were fabricated using three Fe particle size ranges (0–20 µm, 20–40 µm, and 40–80 µm) with varying Fe contents (20–70 wt%), compacted under constant pressure. Combustion performance was evaluated under a fixed single ignition condition. The addition of 2.5 wt% Mg enhanced reactivity and ensured complete and sustained combustion, particularly in compositions with coarse particles or high Fe content.

Beyond burning rate analysis, pellet porosity was measured prior to ignition, and mass changes (loss or gain) were quantified by comparing pellet mass before and after combustion. These data provided insights into the material's conversion efficiency and the influence of ambient atmospheric oxygen on post-combustion mass variation. Combustion repeatability was verified through triplicate testing, with low standard deviations confirming experimental consistency.

The powders were characterized by using Scanning Electron Microscopy (SEM) to assess particle morphology and agglomeration, while Energy Dispersive Spectroscopy (EDS) was used to confirm elemental composition and detect potential surface oxidation or impurities. SEM/EDS observations revealed strong morphological differences between the particle size classes, directly affecting packing density and reaction uniformity.

In conclusion, combining fine Fe particles, a balanced Fe/CuO ratio, and 2.5% Mg doping produced fast, reliable, and reproducible combustion, offering promising potential for advanced thermite-based energetic applications. The resulting data set captures the complex interplay between composition, structure, and ignition behavior in Fe/CuO thermites. It serves as a robust experimental foundation for pyrotechnic laboratories and modelers working on numerical simulation, reaction front propagation, and kinetic parameter extraction in thermite systems.

## 1. Introduction

In recent decades, metal-based combustion systems have received growing attention due to their potential in propulsion, energy generation, and pyrotechnic applications [1,2]. Among the various metal-oxidizer combinations studied, the iron and copper oxide (Fe/CuO) system has emerged as a promising thermite mixture. This system enables heterogeneous solid-phase combustion with favorable features such as mechanical robustness, stable combustion fronts, and low gaseous byproducts [3–9]. These properties are particularly useful in applications requiring controlled burn rates, minimal gas generation,

and structural integrity under varying environmental conditions.

Iron, while offering lower enthalpy of combustion compared to light metals such as aluminum or magnesium, compensates with high thermal stability, resistance to shock and friction, and compatibility with a variety of oxidizers. Gerlich and Wojewódka [9] investigated Fe/BaO₂ compositions and showed that iron-based mixtures offer precise, low-gas combustion, making them suitable for time-delay elements and controlled energetic devices. Panahi et al. [10], in a drop-tube furnace study, revealed that individual iron particles could sustain combustion at elevated temperatures with behavior highly dependent on particle size and the oxidizing environment. Despite its moderate reactivity, iron

<footnote><sup>a</sup> University of Orleans, INSA-CVL, PRISME UR 4229, Bourges, France</footnote>

<footnote><sup>b</sup> University of Orleans, IUT de Bourges, Bourges, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: leo.courty@univ-orleans.fr (L. Courty).</footnote>
maintains a consistent and controllable combustion behavior, which is advantageous for formulations demanding repeatable ignition and steady energy release.

Copper oxide (CuO), the oxidizer component in Fe/CuO thermites, plays a crucial role in determining the ignition temperature, propagation speed, and total energy output of the mixture. Several studies have shown that CuO offers a high oxidation potential and decomposes at relatively low temperatures, releasing oxygen efficiently. Annesini et al. [11] studied the reduction kinetics of CuO in CuO-ZnO systems and observed a two-step mechanism involving reduction to Cu₂O followed by further reduction to Cu. Such findings are directly relevant to Fe/CuO thermites, where the redox progression governs combustion efficiency. Moreover, the particle size and morphology of CuO are key to tuning reactivity. Hosseini et al. [6] demonstrated that nanoscale CuO significantly reduces ignition temperature and activation energy in Mg/CuO thermites due to higher surface area and shorter diffusion paths. These results underline the potential of microstructural optimization in CuO to improve its oxidizing performance, even when paired with less reactive metals like iron.

Building on this, recent works have explored CuO's role in nano-structured thermites. Polis et al. [12] examined Ti/CuO systems, showing that CuO's reactivity and interfacial diffusion behavior significantly influence combustion dynamics. They demonstrated that nano-scale engineering through techniques like wet sonication and electrospray deposition can yield self-propagating combustion with burning velocities exceeding 600 m/s. In their study, cellulose nitrate was added to promote porosity and enhance gaseous diffusion, further accelerating flame propagation. These observations, though focused on titanium-based systems, offer insights transferable to Fe/CuO formulations, especially regarding the design of microstructures and incorporation of additives to optimize reaction fronts.

Magnesium (Mg) has emerged as a particularly promising additive for enhancing the reactivity of iron-based thermites. Owing to its high energy density and low ignition temperature, Mg can act as both a dopant and an ignition facilitator. Its presence can improve flame propagation, reduce ignition delay, and increase overall combustion completeness. Hosseini et al. [6] highlighted that Mg/CuO mixtures benefit significantly from the nanosizing of CuO, leading to more intense and rapid exothermic reactions. Similarly, Jun-Wang Liu et al. [13] studied a dual-oxidant thermite system (Al/Mg with CuO and MoO₃), showing that Mg not only lowered activation energy but also promoted multi-stage combustion, increasing energy output. In our context, incorporating a small amount of Mg into Fe/CuO formulations is expected to mitigate the lower reactivity of iron and facilitate more reliable ignition and combustion propagation.

Despite these promising findings, the influence of Mg doping in Fe/CuO thermite systems has not been extensively studied [14–17]. Most prior investigations have focused on systems dominated by light metals (Al or Mg), with less attention given to Fe-based mixtures [18]. This represents a key knowledge gap, particularly in understanding how small amounts of Mg affect ignition stability, flame velocity, and reaction completeness in iron-rich thermites. Additionally, while many studies emphasize nano-structured materials or reactive multilayers, practical energetic systems often require compacted, pelletized formulations that can be reliably ignited and scaled for real-world use.

Powder morphology and compaction behavior are equally critical to the performance of pelletized thermites. Kurt and Davies [19] analyzed the uniaxial compaction of various metal powders up to 950 MPa and identified three major stages: particle rearrangement, plastic deformation, and strain hardening. They found that irregularly shaped particles had higher compressibility due to better interlocking, while powders with lower initial density achieved higher final compactness. These structural factors affect porosity and thermal conductivity, which in turn influence ignition and flame propagation. The study's implications extend to the processing of Fe/CuO thermites, where packing behavior and density can dramatically alter combustion dynamics.

Fathollahi et al. [20] further examined the influence of particle size on thermal decomposition behavior, revealing that reducing particle size improves reaction rates, sharpens exothermic peaks, and lowers decomposition onset temperatures. These effects are linked to increased interfacial contact and reduced mass transfer resistance. Rosères et al. [21] expanded on these findings by demonstrating that optimized granulometry and chemical composition significantly enhance combustion velocity and repeatability in various pyrotechnic systems. Likewise, Zapata et al. [22] and Zhang et al. [23] stressed the role of formulation porosity and homogeneity in sustaining consistent combustion, even in nano-engineered structures.

Beyond experimental studies, numerical modeling efforts have helped to contextualize the physical phenomena underlying thermite combustion. Tichtchenko et al. [24,25] developed a one-dimensional model for Al/CuO powdered thermites, incorporating heat transfer, fluid flow, and multiphase reactive transport equations. This model successfully reproduced experimental observations and demonstrated the sensitivity of burn rate to factors such as stoichiometry, porosity, and particle size. Though their focus was Al-based systems, the modeling approach is directly applicable to Fe/CuO formulations, especially when evaluating the impact of additives like Mg or variations in compaction. Julien et al. [26] also investigated mechanical influences on combustion dynamics, showing that substrate-induced stresses in multilayer films can significantly affect ignition sensitivity and propagation rates. Their work further supports the idea that structural and mechanical parameters must be considered alongside chemistry in thermite design.

Fischer and Grubelich [27], through thermodynamic analysis, ranked several thermite systems based on adiabatic flame temperatures and total reaction enthalpy. CuO-based systems were identified as energetically favorable due to their high oxidation potential and wide compatibility with various fuels. While aluminum and magnesium offer higher gravimetric energy densities, iron was noted for its superior structural stability, lower sensitivity, and consistent performance under mechanical and thermal constraints. These findings reinforce the potential of Fe/CuO thermites, particularly when doped with Mg to enhance ignition and maintain stable energy output.

Despite the growing interest in Fe/CuO systems, a lack of detailed experimental studies persists concerning the effects of Mg doping and particle size on combustion performance [14–17,28]. This is particularly relevant for the development of practical thermite pellets, where compaction and porosity must be carefully controlled to ensure uniform combustion. The reactive front speed and granulometry of iron particles are critical parameters that directly influence ignition reliability, energy release, and flame propagation.

In this study, we present a detailed experimental investigation of Fe/CuO thermite mixtures, both undoped and doped with 2.5 wt% Mg. We systematically explore the influence of Fe particle size and formulation porosity on combustion front velocity and ignition behavior. Undoped mixtures were tested in triplicate due to frequent extinction events, while Mg-doped compositions exhibited stable ignition and consistent combustion across all Fe concentrations. Complementary measurements, including porosity before ignition and mass variation before and after combustion, provide further insights into combustion completeness and redox efficiency. Morphological and elemental analyses using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) were performed to examine post-combustion structures and validate reaction pathways at the microscale.

By establishing a reproducible and comprehensive experimental dataset, this study aims to clarify the relationship between particle-scale formulation parameters and combustion performance in Fe/CuO thermites. The results not only enhance our understanding of Mg's role as a dopant in iron-rich systems but also provide a solid foundation for future modeling and formulation optimization in scalable, solid-phase energetic materials.
## 2. Experimental device and procedures

### 2.1. Preparation of materials Used

A parametric study was conducted using two primary powders, iron (Fe) and copper oxide (CuO), along with a secondary powder, magnesium (Mg), used as an additive in the different mixtures as shown in Table 1. This study focused on the granulometry of iron from the brut one, which was divided into three classes using sieves: 0 < d < 20 µm: This range represents the finest particles, providing a greater specific surface area. It promotes increased chemical reactivity. 20 < d < 40 µm: This range balances moderate reactivity and particle manageability, reducing agglomeration while preserving a reactive surface, and 40 < d < 80: Coarser particles have a lower specific surface area, reducing reactivity. However, they are less prone to agglomeration, which can affect mixture homogeneity and combustion dynamics. The particle size of the powders was measured by laser particle size analyzer model Spraytec MALVERN.

All powders were supplied by Mon-Droguiste.Com. Key variables in the study included: Iron Granulometry Classes, Iron Concentration, Magnesium (Mg) Addition. To ensure the homogeneity of the reactive mixtures, the powders were first dried in an oven at 70 °C during 24 h before any experimental handling. Once prepared, the powders were carefully mixed to achieve a uniform concentration using a Turbula mixer. The mixtures were then stored as powder compositions in small glass vials, Ready for the various experimental tests, namely pellet formation and ignition.

To assess the reproducibility of the combustion behaviour, three independent ignition tests were performed for the undoped Fe/CuO system under identical conditions (see Table 1). In contrast, the Mg doped Fe/CuO compositions were tested once, as preliminary trials demonstrated highly stable and self-sustained ignition without extinction. The addition of magnesium is used to enhance the reaction kinetics and ensure complete conversion, leading to consistent combustion front propagation across all tested samples. Therefore, a single representative experiment was considered sufficient to characterize the behaviour of the Mg doped compositions.

Regarding the mechanical integrity of the pellets during handling, mixtures containing 10 wt% Fe were found to be mechanically fragile: several pellets partially disintegrated during thickness and mass measurements, preventing reliable characterization. In contrast, pellets with 80 wt% Fe exhibited good mechanical cohesion, although their reactivity remained very low. These observations are reported for completeness, as they reflect practical limitations encountered during sample preparation and handling.

### 2.2. Pellet formation and Setup for ignition

The reactive mixtures were compressed into square-shaped pellets using a uniaxial hydraulic press equipped with an inner piston of 1440 mm², and a 100 mm² die piston (see Fig. 1-(A)). Each pellet weighed approximately 400 mg and was formed under a pressure of 288 MPa to ensure consistency in density and structural integrity. This pressure is calculated using the following formula:

$$P_c = \frac{S_p * P_p}{L^2} \qquad (1)$$

P<sub>c</sub>: Pressure exerted on the pellet, S<sub>p</sub>: Surface of the press piston, L<sup>2</sup>: Surface of the inner piston and P<sub>p</sub>: Pressure from the press gauge (200 bar).

Subsequently, the pellet was weighed before and after ignition to check for any gas release or material degradation.

The ignition source was a butane torch producing a conical blue flame with a manufacturer-specified temperature of approximately 1300 °C (RS PRO MT790, 467–450 mini gas torch). According to the technical datasheet, this maximum flame temperature is achieved under fully aerated conditions. The gas flow was adjusted to produce a stable and well-defined blue flame, approximately 15 mm in height with a base diameter of about 3 mm under maximum aeration. The tip of the inner blue cone assumed to correspond to the hottest point of the flame was positioned in direct contact with the lateral surface of the pellet to ensure controlled heating over an area of approximately 10 mm × 1 mm. The flame to-pellet distance was maintained at 0 ± 0.5 mm throughout all experiments.

During ignition, the tip of the inner blue cone was first moved slowly along the lateral surface of the pellet to ensure homogeneous heating over the entire 10 mm facet. After the onset of the reaction front, the flame was then moved away from the pellet to avoid influencing the propagation dynamics.

Ignition exposure time was estimated at max 5 ± 1 s for the primary ignition and 2 ± 1 s for the secondary ignition condition, in cases where re-ignition was necessary. These parameters correspond to optimized operating settings that ensured initiation of the thermite pellets. The extinction time is defined as the precise moment at which the luminous reaction front completely stops propagating across the sample, corresponding to the disappearance of the luminous signal in the video recordings. Therefore, this extinction time is considered a single temporal point (t<sub>ext</sub>), rather than a duration (see figure 2: ignition-1 and ignition-2). All ignition tests were carried out under the same torch operating conditions. Ignition exposure time was estimated at max 5 ± 1 s for the primary ignition and 2 ± 1 s for the secondary ignition condition, in cases where re-ignition was necessary. These parameters correspond to optimized operating settings that ensured initiation of the thermite pellets. The extinction time is defined as the precise moment at which the luminous reaction front completely stops propagating across the sample, corresponding to the disappearance of the luminous signal in the video recordings. Therefore, this extinction time is considered a single temporal point (t<sub>ext</sub>), rather than a duration (see figure 2: ignition-1 and ignition-2). All ignition tests were carried out under the same torch operating conditions.

During the first ignition tests, the pellets were at ambient temperature (~20 °C). In contrast, the second ignition occurred under preheated conditions due to residual heat from the initial combustion. No systematic temperature measurements were performed during ignition; only an indicative value of approximately 120 °C was recorded for one representative case (70 wt% Fe, 20 < D < 40 µm), and is reported here solely as a qualitative reference. A more detailed temperature analysis based on spectroscopic diagnostics will be investigated in a subsequent study.

<table><caption>**Table 1**

Experimental design for the various mixtures investigated.</caption><thead><tr><th>Mixture type</th><th>Iron granulometry class (D<sub>Fe</sub>)</th><th>Iron concentration (%)</th><th>(Fe + CuO) Mass (mg)</th><th>Mg additive (mg)</th><th>Applied pressure (MPa)</th><th>Repetitions</th></tr></thead><tbody><tr><td>Fe + CuO</td><td>0 &lt; D &lt; 20 µm</td><td>20, 30, 40, 45, 50, 60, 70</td><td>400</td><td>0</td><td>288</td><td>3(per concentration)</td></tr><tr><td>Fe + CuO</td><td>20 &lt; D &lt; 40 µm</td><td>20, 30, 40, 45, 50, 60, 70</td><td>400</td><td>0</td><td>288</td><td>3(per concentration)</td></tr><tr><td>Fe + CuO</td><td>40 &lt; D &lt; 80 µm</td><td>20, 30, 40, 45, 50, 60, 70</td><td>400</td><td>0</td><td>288</td><td>3(per concentration)</td></tr><tr><td>Fe + CuO + Mg</td><td>0 &lt; D &lt; 20 µm</td><td>20, 30, 40, 45, 50, 60, 70</td><td>390</td><td>10</td><td>288</td><td>1(per concentration)</td></tr><tr><td>Fe + CuO + Mg</td><td>20 &lt; D &lt; 40 µm</td><td>20, 30, 40, 45, 50, 60, 70</td><td>390</td><td>10</td><td>288</td><td>1(per concentration)</td></tr><tr><td>Fe + CuO + Mg</td><td>40 &lt; D &lt; 80 µm</td><td>20, 30, 40, 45, 50, 60, 70</td><td>390</td><td>10</td><td>288</td><td>1(per concentration)</td></tr></tbody></table>
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** (A): Diagram illustrating the principle of stress calculation and the three-step pelletizing process. (B): Setup for visualizing ignitions and tracking the reactive front of combustion. (C): Setup of the first ignition and the second ignition if extinction occurs.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Sequence of images showing the two ignition events for the 20% Fe + 80% CuO composition. (Red arrow: Extraction direction for determining the flame front position. White line: Location or propagation of the reaction front. Yellow area: Indicates the reacting part of the pellet.). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
This thermal pre-conditioning significantly affected reactivity and shortened the ignition delay during the second ignition sequence. The high-speed camera provides several acquisition modes. In the mode used for the experiments (HS 1000 fps), the recorded resolution is 224 × 160 pixels. At a camera-to-target distance of 150 mm, the calibrated field of view covers 55 mm × 39 mm, resulting in a spatial resolution of approximately 0.245 mm per pixel. Under these imaging conditions, the corresponding angular field of view is approximately 20.8° horizontally, 14.8° vertically, and 25.3° diagonally, ensuring sufficient spatial detail to capture the reaction front dynamics despite the high frame rate. A transparent shield was used to protect the camera optics from hot gases and particle projections.

The setup allowed precise visualization and temporal resolution of the combustion dynamics (see Figs. 2 and 3), including burning rate, total combustion duration, and extinction events. To analyze the combustion frames, a custom image-processing program developed in the laboratory was used to extract quantitative information from video sequences, including the combustion front velocity (burning rate) and reaction time for each test, The propagation length was extracted manually at successive time steps from the image sequence. In the corresponding figures (2 and 3), the red arrows schematically indicate the direction of propagation, while the distance travelled by the combustion front is shown by the thin white line measured in each frame.

## 2.3. SEM-EDS instrumentation and sample preparation

Scanning Electron Microscopy and Energy-Dispersive X-ray Spectroscopy (SEM-EDS) analyses were carried out using a Zeiss Sigma 300-07-38 microscope operated at an accelerating voltage of 20 kV. A 60 µm condenser aperture was used to set the probe current and beam spot size. The extraction voltage was 3.80 kV, with an extraction current of 170 µA and a filament current of 2.39 A. The column vacuum was maintained at 1.88 × 10⁻⁹ mbar, while the chamber vacuum at sample level was approximately 10⁻⁶ mbar. The instrument was operated using the SmartSEM 6.00 software.

EDS analyses were performed with an Oxford Instruments detector controlled by AZtec. Elemental maps were acquired at 2048 × 1577 pixels, with a total of approximately 2 × 10⁶ accumulated counts per map to ensure sufficient statistical accuracy. The detector was energy calibrated using a cobalt reference standard prior to acquisition.

Pellets were embedded in epoxy resin and mechanically polished using SiC abrasive papers (P1200), followed by a final polishing step. A dry-air blow was then applied to eliminate polishing debris and traces of silicon originating from the SiC paper. This preparation ensured a flat and mechanically stable surface for cross-sectional SEM-EDS analyses with minimal contamination. In this study, all visualisations are derived from volumetric cross sections. These sections were taken in the mid-plane of the pellet, approximately 4 to 5 mm from the outer edge, in

order to reduce the influence of external environmental disturbances. Surface measurements were deliberately excluded, as they are much more sensitive to ambient conditions and therefore less representative of the internal behaviour of the sample.

SEM-EDS was then used to characterize the pellets before and after combustion. SEM provided high-resolution morphological imaging, while EDS enabled elemental mapping and compositional assessment, allowing detailed analysis of microstructural evolution and redox progression during the combustion process.

## 2.4. Porosity calculation

To determine the porosity of the compressed Fe/CuO (or Fe/CuO-Mg) pellets, 400 mg of powder mixture were pressed under a pressure of 200 bar using a square die with a cross-sectional area of 1 cm². The compact height (h) was measured after pressing in order to calculate the experimental density ($ρ_e$) according to equation (2):

$$ρ_e = \frac{m}{V} = \frac{m}{S * h} \qquad (2)$$

Where m is the mass of the sample (0.400 g) and S is the cross-sectional area of the die (1 cm²). The theoretical density ($ρ_t$) of the mixture was calculated based on the rule of mixtures using equation (3), taking into account the weight fractions ($w_i$) and theoretical densities ($ρ_i$) of each component:

$$ρ_t = \sum_i w_i ρ_i \qquad (3)$$

Finally, the porosity (P) of the compact was determined from the difference between the theoretical and experimental densities using equation (4):

$$P = 100 * \left( 1 - \frac{ρ_e}{ρ_t} \right) \qquad (4)$$

This approach allows evaluation of the relative packing efficiency and void fraction in the pressed thermite pellets at different compositions.

## 2.5. Light diffraction for characterization of iron granulometry

This graph (Figs. 4 and 5) shows the particle size distribution based on volume percentage of the lot of the different powders performed by Spraytec laser particle size analyzer from Malvern Instruments. The x-axis (logarithmic scale) represents the diameter of particles in micrometers (µm). The blue bars represent the volume percentage of particles within specific size classes this is called the class volume distribution. The red curve shows the cumulative volume distribution, which indicates the percentage of total volume made up by particles smaller than a given size. Most particles in the primary iron powder are concentrated

<figure><img src="image_4.png" /><figcaption>Fig. 3. Sequence of images showing a single ignition event without extinction for the 69.25% Fe + 29.25% CuO + 2.5% Mg composition. (Red arrow: Extraction direction for determining the flame front position. White line: Location or propagation of the reaction front. Yellow area: Indicates the reacting part of the pellet.) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 4. Particle size distribution of the lot of primary iron powder and the sieved iron classes.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Particle size distribution of the primary iron, the lot of the copper oxide and the additive magnesium.</figcaption></figure>

in the 10–100 µm range, where the blue histogram peaks. This indicates that the bulk of the material consists of medium-sized particles.

The cumulative curve rises steeply in this same range, meaning a large portion of the volume is contributed by these particle sizes. At around 100 µm, the cumulative distribution approaches 100%, meaning nearly all particles are smaller than this size. The characteristics of the other sieved powders iron, copper oxide and magnesium are reported in Figs. 4 and 5. The full statistical analysis is summarized in Table 2.

<table><caption>**Table 2**

Statistical analysis of the particle size distribution of the powders used.</caption><thead><tr><th>Variable</th><th>Primary<br>iron<br>powder</th><th>Fe D &lt;<br>20 µm</th><th>20 &lt; Fe<br>D &lt; 40<br>µm</th><th>40 &lt; Fe<br>D &lt; 80<br>µm</th><th>CuO<br>D µm</th><th>Mg D<br>µm</th></tr></thead><tbody><tr><td>Dv(10)</td><td>10.21</td><td>13.26</td><td>21.02</td><td>26.65</td><td>1.54</td><td>13.68</td></tr><tr><td>Dv(50)</td><td>38.10</td><td>24.63</td><td>34.43</td><td>44.70</td><td>3.44</td><td>36.27</td></tr><tr><td>Dv(90)</td><td>70.20</td><td>45.97</td><td>55.09</td><td>73.20</td><td>9.88</td><td>79.15</td></tr></tbody></table>

## 2.6. SEM characterization of materials Used

**Iron:**

Fig. 6 shows Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) images of the iron (Fe) powder for three different particle size ranges:

Top row A-B (0 < D < 20 µm): The full size distribution displays irregular and dispersed particles. EDS mapping confirms the dominance of iron, with minor traces of oxygen and other elements, however, oxygen and carbon signals should be interpreted qualitatively, as EDS does not accurately quantify light elements. Middle row C-D (20 < D < 40 µm): Particles appear more uniform and slightly larger than those in the previous range. EDS analysis shows a consistent Fe distribution, while slight oxygen signals likely linked to surface oxidation are only indicative due to the limitations of EDS quantification for light elements. Bottom row E-F (40 < D < 80 µm): Larger and more defined particles with smoother surfaces are observed. EDS mapping continues to highlight Fe as the main element, with localized signals corresponding to
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) images of primary iron (Fe) powder for three different particle size ranges. (A): Magnification × 400, Fe D < 20 µm, (B): ×1600, Fe D < 20 µm, (C): ×400, 20 < Fe D < 40 µm, (D): ×1600, 20 < Fe D < 40 µm, (E): ×400, 40 < Fe D < 80 µm, (F): ×1600, 40 < Fe D < 80 µm.</figcaption></figure>

trace elemental superpositions, acknowledging that light-element quantification remains approximate.

**Copper oxide (CuO)**

Fig. 7 presents the morphological and elemental analysis of a black copper oxide (CuO) powder sample. The SEM image reveals a morphology consisting mainly of spherical to quasi-spherical particles, exhibiting significant agglomeration. The average particle size is

estimated to be approximately 1 to 4 µm.

The EDS elemental mapping, performed on the same region, shows a homogeneous distribution of the constituent elements. Copper (in red) and oxygen (in yellow/orange) from the superposition of red (Cu) + green (O) are uniformly distributed across the analyzed area, confirming the composition of CuO. The carbon signal originates from the adhesive tape used to hold the powder sample in place. No significant traces of

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) images of the copper oxide used. (G): Magnification × 6400 and (H): ×10 000.</figcaption></figure>
elemental impurities were detected, indicating a high purity level of the
synthesized material.

**Magnesium:**

Fig. 8 presents SEM and EDS analyses of magnesium (Mg) powder at different magnification. The SEM image (left) shows irregular, flake-like particles with smooth surfaces, typical of mechanically processed magnesium powders.

The EDS elemental map (Fig. 8, right) reveals a homogeneous dis-
tribution of magnesium. The green areas observed in the map are
attributed to surface oxidation, likely corresponding to a thin layer of
magnesium oxide (MgO) formed during exposure to air.

**3. Experimental results**

3.1. Porosity and mass measurements before and after ignition

Porosity plays a central role in powder-based materials because it
directly governs packing density, mechanical cohesion, and heat trans-
fer. In Fe/CuO mixtures, the initial porosity depends strongly on the iron
content: iron particles undergo plastic deformation under compaction,
promoting densification, while higher CuO fractions lead to more open
structures. In this study, pellets were compacted at 288 MPa to quantify
how the initial porosity varies with Fe concentration for the three par-
ticle size classes investigated. This relationship is particularly relevant
for thermite systems, where the pore network controls both thermal
feedback and gas transport during combustion. Understanding this
initial microstructure is therefore essential for interpreting the subse-
quent reaction behavior and flame front stability.

At low iron concentrations, the metallic particles exhibit a less ho-
mogeneous and less dense structure. This leads to higher porosity
(~40%) because the contact forces between particles are insufficient for
complete compaction, leaving interparticle voids. As the iron concen-
tration increases, particle densification becomes more efficient, and
porosity decreases to approximately 32%. The ductile nature of iron
facilitates plastic deformation and stronger interparticle bonding under
pressure, promoting closer packing and reducing the remaining voids.

The three iron powders studied exhibit a similar trend in terms of porosity, as shown in Fig. 9 (A, B, C). The evolution of porosity as a function of iron concentration under a compaction pressure of 288 MPa shows a direct correlation between iron content and material density. Higher iron concentrations promote more uniform densification and a reduction in porosity, whereas lower iron concentrations result in higher porosity, which can compromise the mechanical integrity of the pellets.

To assess the influence of structural variability on combustion
behaviour, porosity dispersion was evaluated at the pellet scale using
three replicate samples for each composition. The measured dispersions
range from ±1.5% to ±3.0% (see Fig. 9-A–C), which corresponds to a
mass gain/loss dispersion of approximately ±0.1 to ±0.7% (see Fig. 9-
D–F). These values indicate that the variability observed in combustion
parameters, such as mass gain/loss, is mainly governed by the sensitivity

of the combustion process to local microstructural heterogeneities
rather than by measurement uncertainty or systematic differences be-
tween samples. For example, an initial mass of 400 ± 5 mg illustrates
that the dispersion of the initial mass, caused by pellet removal from the
mold, represents only a limited contribution to the overall measurement
uncertainty.

The mass measurements before and after ignition are crucial in un-
derstanding the extent of the reaction. As shown in Fig. 9 (D, E, F), for Fe
+ CuO mixtures with iron concentrations below 45%, a net mass loss is
observed. Between 45% and 60% Fe, the samples exhibit minimal mass
variation, while above 60% Fe, a clear mass gain is detected. The
dispersion observed in both porosity and mass variation is typical for
porous media and arises from the morphology of the metallic and oxide
particles (irregular geometries, agglomeration), which makes it difficult
to reproduce identical packing and contact configurations in each
sample. Nevertheless, this dispersion remains relatively low, approxi-
mately 3% for porosity at 70% Fe (40 < D < 80 µm) and about 1.5% for
mass loss at 20% Fe (40 < D < 80 µm).

**3.2. Combustion behaviour and influence of ignition conditions and**
**particle size**

The results presented in this section are based on a single represen-
tative experimental test to ensure clarity and to avoid overloading the
figures with excessive results.

Fig. 10-A-1 and 10-A-2 illustrate the evolution of the burning rate (front velocity) of Fe/CuO pellets as a function of position along the pellet, for two ignition conditions (Ignition-1 and Ignition-2). All pellets were compacted at 2880 kg/cm² and composed of fine powders (D < 20 µm). The iron content varied from 20% to 70%, which led to corresponding changes in initial porosity. In both ignition regimes, the velocity of the reactive front strongly depends on iron content and porosity.

Under Ignition-1, corresponding to lower initial temperature
(ambient), front velocities are generally smaller (~6 mm/s) and exhibit
more pronounced fluctuations, particularly for low Fe compositions
(20–40%). Highly porous samples (e.g., 20% Fe, 40.5% porosity) show
slow and unstable fronts, reflecting limited thermal conduction and poor
interfacial contact between fuel and oxidizer.

In contrast, Ignition-2, characterized by a higher initial temperature
from the preceding ignition, produces smoother and faster propagation
(~15 mm/s). The effect of increasing Fe content becomes clearer, with
the 40% Fe sample (porosity ≈ 39%) reaching the highest front velocity.
Extinction points marked on the curves reveal that compositions with
moderate porosities (≈35-39%) maintain combustion over longer dis-
tances, while mixtures that are too porous extinguish early.

The temporal curves in Fig. 10-A-3 and 10-A-4 complement the
spatial data by identifying extinction times. Under Ignition-1, combus-
tion is slower and less stable, particularly for pellets containing 20–40%
Fe, which often extinguish before complete pellet consumption. Higher

<figure><img src="image_9.png" /><figcaption>**Fig. 8.** Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) images of the magnesium used for doping. (I): Magnification × 400 and (J): ×1600.</figcaption></figure>
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 9. Porosity and mass gain/loss of the pellets studied respecting the iron granulometry distribution.</figcaption></figure>

Fe contents (60–70%) yield longer burning durations but still show gradual velocity decay. Under Ignition-2, extinction points are delayed or absent for pellets with higher Fe content, which typically sustain burning until full consumption within less than one second.

The effect of iron particle size was examined for three granulometric classes, fine (D < 20 µm), intermediate (20 < D < 40 µm), and coarse (40 < D < 80 µm), under both ignition conditions (see Figs. 10-12). Under low temperature ignition (Ignition-1), front velocity decreases markedly with increasing particle size. Pellets composed of fine powders show the highest and most stable propagation rates for Fe contents above 50%. Intermediate-sized powders display lower burning rates

(4–6 mm/s) and frequent early extinction, while coarse powders experience the greatest limitations, with weak propagation and systematic extinction. At higher ignition temperature (Ignition-2), these limitations are partially overcome. Increased thermal input enables the reactivation of systems containing medium-sized particles (20 < D < 40 µm), particularly for Fe ≥ 50%, achieving burning rates comparable to those of fine powders. However, extinction persists at low Fe concentrations, and the coarsest powders continue to exhibit restricted, irregular combustion. Overall, these measurements highlight the combined influence of Fe content, porosity, ignition energy and particle size on combustion stability in Fe/CuO thermites.
<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 10.** Burning rate as a function of position and time for Fe + CuO pellets compacted at 2880 kg/cm² with iron particles in the size range 0 < Fe D < 20 µm.</figcaption></figure>

Figs. 10-12 (A-C-1)/(A-C-2) and (A-C-3)/(A-C-4) present the same combustion dynamics viewed from two complementary perspectives: the position-based representation highlights local stability or extinction zones along the pellet, whereas the time-based representation emphasizes ignition, acceleration, and the evolution of the average burning rate.

### 3.3. Repeatability of the experimental results

Fig. 13(a–f) presents the evolution of the average burning rate of Fe/CuO pellets as a function of iron content and porosity for two ignition conditions (first and second ignition) and three iron particle size ranges (D < 20 µm, 20–40 µm, and 40–80 µm). Each data point represents the mean value of three repeated experiments, with error bars corresponding to the standard deviation, allowing the reproducibility and variability of the measurements to be assessed.

Across all particle sizes, burning rates are systematically higher under second-ignition conditions, highlighting the influence of ignition energy on combustion propagation. For fine powders (Fig. 13a), the highest burning rates are obtained close to the stoichiometric composition, around 31.9 wt% Fe ($\phi \approx 1$). In this region, larger error bars are

also observed, indicating a greater sensitivity of the combustion behaviour to local microstructural heterogeneities.

Intermediate powders (Fig. 13b) exhibit similar trends but with a noticeable shift in the position of the maximum burning rate: peak values are observed around 45 wt% Fe under second-ignition conditions, whereas the maximum occurs near 40 wt% Fe for the first ignition. For coarse powders (Fig. 13c), burning rates are significantly lower, typically around 6–8 mm/s, and show a weaker dependence on iron content. Two local maxima can nevertheless be identified, one near 30 wt% Fe and another around 45 wt% Fe considering the second ignition.

The evolution of burning rate must be interpreted as a combined effect of iron content and porosity, which vary together during pellet preparation. Combustion velocity generally increases with porosity up to approximately 37–38%, beyond which it decreases, particularly for Fe-lean formulations. Maximum velocities are therefore obtained for mixtures combining moderate porosity with iron contents close to the optimal ranges identified for each particle size. At low iron contents, increasing porosity alone is not sufficient to achieve high burning rates.

Overall, these results confirm that both %Fe and porosity jointly control combustion behaviour, while particle size mainly affects the absolute level of burning rate through modifications of specific surface
<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /><figcaption>**Fig. 11.** Burning rate as a function of position and time for Fe + CuO pellets compacted at 2880 kg/cm² with iron particles in the size range 20 < Fe D < 40 µm.</figcaption></figure>

area and reaction kinetics.

### 3.4. Effect of 2.5% Mg doping on the combustion behaviour of Fe/CuO thermites

Fig. 14 presents the average burning rate of Fe/CuO pellets doped with 2.5% magnesium, as a function of iron content, for three different iron particle size ranges: 0 < D < 20 µm (red triangles), 20 < D < 40 µm (blue squares), and 40 < D < 80 µm (black circles). All tests were conducted under a single ignition condition, and no extinction was observed, even in coarse particle systems.

The addition of Mg leads to a marked improvement in combustion performance across all granulometries. In Mg doped mixtures (2.5 wt% Mg), a pronounced maximum in the burning rate is observed around 45–50 wt% Fe, which corresponds to a near-stoichiometric balance between the total fuel (Fe + Mg) and the oxidizer (CuO), as shown in Fig. 14. Although the optimum remains close to the stoichiometric Fe/CuO ratio (φ ≈ 1), a slight shift toward iron-rich compositions is noticeable, with peak propagation rates obtained for φ ≈ 1.9. Fine powders exhibit the highest performance (≈14.5 mm/s, more than a 100% increase compared to the undoped equivalent), intermediate

particle sizes also show efficient and reproducible propagation, while coarse powders remain slower but still ensure stable combustion.

### 3.5. EDS mapping analysis of Fe/CuO composites before and after ignition

Figs. 15 and 16 present EDS elemental maps for mixtures consisting of 30% Fe / 70% CuO and 70% Fe / 30% CuO (D(Fe) < 20 µm), before and after ignition. Before ignition, the maps reveal a dense and homogeneous distribution of CuO particles with Fe particles more sparsely distributed. At high magnification, the clear separation between CuO and Fe regions confirms that no significant interdiffusion occurs prior to thermal activation.

After ignition, the morphology undergoes significant changes. The Cu signal becomes dominant and continuous, and green regions corresponding to iron oxides (FexOy) appear. In the 30% Fe mixture, numerous cavities and voids (black regions) are observed, while in the 70% Fe mixture, the structure remains largely intact and no visible porosity or cavities are present.

Figs. 17 and 18 present EDS mappings before and after ignition for two Fe/CuO thermite mixtures containing 2.5 wt% Mg, with Fe/CuO
<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /><figcaption>Fig. 12. Burning rate as a function of position and time for Fe + CuO pellets compacted at 2880 kg/cm² with iron particles in the size range 40 < Fe D < 80 um.</figcaption></figure>

ratios of 29.25/69.25 and 69.25/29.25. Before ignition, the systems exhibit homogeneous distributions of Fe and CuO particles, with Mg appearing as small domains, slightly more localized near interfaces in the CuO-rich mixture. After ignition, a significant increase in porosity is observed in the CuO rich system, while the Fe-rich system remains more compact, with fewer pores. In both cases, metallic Cu is found in continuous or coalesced domains, and iron oxides (FexOy) are clearly visible as reaction products. MgO is observed preferentially at the interfaces between Cu and FexOy regions. Traces of silicon (Si) are occasionally detected and attributed to surface contamination from the abrasive polishing, not to the redox mechanism itself.

For mixtures containing 2.5 wt% Mg with an Fe/CuO ratio of 29.25/69.25, the pellet exhibits a markedly different evolution compared with the Mg free samples. Cross sectional observations show that the pellet progressively loses its initial geometry, passes through a transient liquid-like state during the reaction, and ultimately resolidifies into a significantly altered morphology. This behaviour constitutes a major structural transformation, far beyond simple pore rearrangement, and is fully consistent with the enhanced reactivity induced by Mg addition. The qualitative evidence presented here is sufficient to establish the distinct transformation pathway associated with Mg, while a detailed quantitative characterisation of pore evolution will be addressed in a dedicated

study.

# 4. Discussion

## 4.1. Porosity, Fe content and mass variation

The transition from mass loss at low Fe content to mass gain at high Fe content (Fig. 9) reflects the competition between gas release and post reaction oxidation. For Fe contents below about 45 wt%, the net mass loss is consistent with oxygen release during CuO reduction and with the possible formation of volatile or gaseous species. Above 60 wt% Fe, the positive mass change can be attributed to oxygen uptake from ambient air during or after the reaction. This behavior corresponds to the partial oxidation of metallic iron, according to the following reactions (5) and (6):

$$4\text{Fe} + 3\text{O}_2 \rightarrow 2\text{Fe}_2\text{O}_3 \quad (5)$$

$$3\text{Fe} + 2\text{O}_2 \rightarrow \text{Fe}_3\text{O}_4 \quad (6)$$

Such oxidation is consistent with the classical oxidation mechanism described by Cabrera et al. [29], who demonstrated that iron exposed to elevated temperatures in air develops protective oxide layers through a
<figure><img src="image_28.png" /><figcaption>Fig. 13. Average burning rate as function of iron concentration and porosity.</figcaption></figure>

diffusion-controlled oxidation process. Likewise, Zhang et al. [30] re-
ported that residual metallic iron in Fe based systems undergoes rapid
post reaction oxidation when exposed to atmospheric oxygen, resulting
in the formation of Fe₂O₃/Fe₃O₄ scales and a measurable mass gain.
These consistent observations confirm that Fe rich thermite formula-
tions are prone to secondary oxidation during the cooling stage.

The relatively low dispersions observed in porosity (±1.5–3%) and
mass change (±0.1–0.7%) indicate that the trends observed in burning
rate are governed primarily by the intrinsic sensitivity of combustion to
local microstructural heterogeneities rather than by large scale vari-
ability between nominally identical pellets.

The nonlinear dependence between porosity and burning rate
highlights the combined influence of structural accessibility and reac-
tion enthalpy. The turning point near ~ 45 wt% Fe reflects an optimum
between heat release and thermal dissipation. In Fe lean mixtures,
higher porosity cannot compensate for insufficient available fuel.

Beyond the initial porosity, part of the post combustion voids arises
from high temperature microstructural evolution of Fe domains,
including thermomechanical shrinkage and solid state sintering, occa-
sionally accompanied by localized oxygen release. These mechanisms
explain the irregular void morphologies and their preferential occur-
rence near Fe rich regions and Fe/Cu interfaces.

4.2. Influence of ignition conditions and particle size on combustion regimes

The strong dependence of burning rate on ignition conditions and particle size (Figs. 10-13) is consistent with previous studies on thermite and nanothermite systems [31–33]. Under higher ignition energy (Ignition-2), the observed increase in burning rate and reduction in extinction frequency confirm that thermal input enhances front propagation by improving heat feedback and energy coupling within the
<figure><img src="image_29.png" /><figcaption>Fig. 14. Burning Rate of Mg-Doped Fe/CuO Thermite Pellets vs Fe Content for Different Iron Particle Sizes.</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>Fig. 15. SEM-EDS Analysis of 30%Fe + 70%CuO Thermite Pellets (Fe particles, D < 20 µm). Before Combustion (A): Magnification × 200, (B): ×1600, and After Combustion (C): ×100, (D): ×1600.</figcaption></figure>

reaction zone, as demonstrated by Brotman et al. (2021) [34] and Weismiller et al. (2009) [35].

For fine powders, the large error bars near the burning rate maximum under strong ignition suggest that local structural heterogeneities (porosity, agglomeration) substantially affect front stability. This is in line with Saceleanu et al. (2018) [36], who reported increased burning rate dispersion in loosely compacted Al/CuO nanothermites, and with Shi et al. (2024) [37], who discussed the role of agglomeration and discontinuous phase formation in reducing combustion reliability. Intermediate powders display smoother and more reproducible behavior, indicating a compromise between surface area and structural integrity, similar to the stable self propagation observed by Wang et al. (2021) [38] in highly homogeneous Al/CuO systems. In contrast, the flat

burning rate profiles of coarse powders point to diffusion controlled combustion, limited by reduced interfacial contact and lower effective thermal conductivity, as also suggested by Collins et al. (2013) [39] and Saceleanu et al. [36]. Overall, the experimental trends align with the picture that optimal behavior is achieved near a slightly fuel rich composition with moderate porosity, where structural robustness and thermal feedback are jointly maximized.

### 4.3. Influence of ignition energy, structural heterogeneity, and thermal history

The systematically higher burning rates observed during second ignition demonstrate that front propagation is strongly influenced by the
<figure><img src="image_31.png" /><figcaption>**Fig. 16.** SEM-EDS Analysis of 70%Fe + 30%CuO Thermite Pellets (Fe particles, D < 20 µm). Before Combustion (A): Magnification × 200, (B): ×1600, and After Combustion (C): ×100, (D): ×1600.</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>**Fig. 17.** SEM-EDS Analysis of 29.25%Fe + 69.25%CuO + 2.5%Mg Thermite Pellets (Fe particles, D < 20 µm). Before Combustion (A): Magnification × 200, (B): ×1600, and After Combustion (C): ×100, (D): ×1600.</figcaption></figure>

thermal energy available at initiation. Increased ignition energy en-
hances heat feedback and reactive coupling within the combustion zone,
leading to faster and more stable propagation, in agreement with the
findings of Brotman et al. (2021) [34] and Weismiller et al. (2009) [35].
This sensitivity to ignition energy also reflects the influence of structural
heterogeneity: the large error bars measured for fine powders near the
burning rate maximum are consistent with observations by Saceleanu
et al. (2018) [36] and Shi et al. (2024) [37], who showed that loosely
compacted or agglomerated microstructures generate significant

variability in heat transfer and front stability.

The marked improvement in burning rates during second ignition further indicates that the reaction is responsive to the thermal history of the material. Partial preheating or microstructural rearrangement induced by the first ignition likely enhances particle connectivity and reactive pathways, thereby reducing extinction probability and promoting more continuous combustion. Together, these results confirm that both the applied ignition energy and the evolving microstructure play a central role in controlling thermite front propagation.
<figure><img src="image_33.png" /><figcaption>Fig. 18. SEM-EDS Analysis of 69.25%Fe + 29.25%CuO + 2.5%Mg Thermite Pellets (Fe particles, D < 20 µm). Before Combustion (A): Magnification × 200, (B): ×1600, and After Combustion (C): ×200, (D): ×1600.</figcaption></figure>

## 4.4. Effect of particle size on reaction regime

Intermediate sized powders show smoother and more repeatable behavior, consistent with findings from Wang et al. (2021) [38], where homogeneous microstructures led to stable front propagation. In contrast, the flat burning rate profile observed for coarse powders indicates a predominantly diffusion-controlled regime, where limited interfacial contact restricts the reaction rate. This agrees with Collins et al. (2013) [39], who showed that reduced thermal conductivity suppresses reactive propagation in similar systems.

## 4.5. Formation of pores during the combustion

Cross section imaging before and after combustion (Figs. 15-18) shows that the as pressed pellets contain small interparticle voids, while cavities formed after combustion can reach ~ 200 µm. Their enlargement results from the interaction between initial porosity and the thermal evolution of the reacting solid, leading to partial densification or softening of Fe oxide regions (FexOy). In Fe lean areas, microscale deviations from the nominal Fe/CuO ratio may generate excess oxygen once Fe becomes fully oxidized, which can remain locally trapped and contribute to cavity growth. As porosity evolution is not quantified in this work, these interpretations remain qualitative.

Most post combustion cavities occur within Fe rich regions or at Fe/Cu boundaries. Their irregular, non spherical shape indicates a predominantly solid-state origin. Studies on Fe combustion (Ning et al., 2022; Choisez et al., 2023) [40,41] show that FeOx liquids when they form produce nearly spherical pores during solidification. Because such features are absent here, Fe likely remains solid under the present thermite conditions, although localized transient FeOx liquid formation cannot be excluded. Copper, which melts at 1085 °C, redistributes in the liquid state during combustion, forming compact Cu rich zones with limited porosity. As previously shown in Section 3.5, the Cu signal becomes continuous after reaction, confirming extensive CuO reduction into metallic Cu according to the thermite-like reactions:

$$ \mathrm{CuO}(\mathrm{s}) + \mathrm{Fe}(\mathrm{s}) \rightarrow \mathrm{Cu}(\mathrm{l}) + \mathrm{FeO}(\mathrm{s}) \quad (7) $$

$$ 3 \mathrm{CuO} + 2 \mathrm{Fe} \rightarrow 3 \mathrm{Cu} + \mathrm{Fe}_{2} \mathrm{O}_{3} \quad (8) $$

These reactions simultaneously confirm oxidation of Fe by oxygen transfer from CuO. This explains the dense post combustion microstructures in Fe rich mixtures (70 wt% Fe), where the global redox balance does not promote oxygen supersaturation or pore formation.

In a stoichiometric Fe/CuO thermite mixture, oxygen released during CuO reduction is fully consumed by Fe oxidation, resulting in no net production of gaseous oxygen. However, under Fe lean or CuO rich local conditions, once metallic Fe is fully oxidized, further reduction of CuO may proceed through intermediate reactions:

$$ 2 \mathrm{CuO} + \mathrm{RIGARW} \mathrm{Cu}_{2}\mathrm{O} + \frac{1}{2} \mathrm{O}_{2} \quad (9) $$

$$ 4 \mathrm{CuO} + \mathrm{RIGARW} \mathrm{2Cu}_{2}\mathrm{O} + \mathrm{O}_{2} \quad (10) $$

Thermodynamic data reported by Hu et al., (2016) show that this reversible decomposition becomes favorable between 850 and 1000 °C [42], depending on the local oxygen partial pressure.

In such non stoichiometric microvolumes, oxygen transport toward Fe may become kinetically limited, allowing transient O2 accumulation. If this oxygen remains trapped within a partially softened oxide network, it may generate local overpressure and contribute to cavity formation.

This effect is further enhanced in Mg doped Fe lean systems, where the additional heat released by Mg oxidation increases local temperature and oxygen mobility, thereby promoting CuO reduction beyond the capacity of Fe to accommodate oxygen. These mechanisms remain local and do not contradict the overall redox balance of the Fe/CuO thermite system.

## 4.6. Effect of Mg addition on combustion and microstructure

The addition of 2.5 wt% Mg significantly improves combustion performance and eliminates extinction, even for coarse powders (Fig. 14). Magnesium acts as an energetic additive, providing supplementary heat through its high oxidation enthalpy and facilitating ignition owing to its low activation threshold, as reported by Hosseini et al. (2016) [6] and Brotman et al. (2021) [34].
For Mg containing mixtures, the effective fuel to oxidant ratio $\varphi$ was recalculated by including Mg as an additional fuel component. For a Mg content of 2.5 wt%, the global $\varphi$ remains close to unity at stoichiometric conditions, while the maximum burning rate shifts toward $\varphi \approx 1.9$, reflecting the additional heat released by Mg oxidation.

The shift of the optimal burning rate toward slightly Fe rich compositions ($\varphi \approx 1.9$) while remaining close to the Fe/CuO stoichiometric ratio is consistent with the additional heat released by Mg oxidation, which increases the local reaction temperature and allows sustained front propagation under moderately fuel rich conditions.

The SEM/EDS observations further show that Mg addition enhances porosity formation in CuO rich systems and promotes the formation of MgO at interfaces between Cu and FexOy (Figs. 17-18). This behavior supports a role of Mg as an interfacial facilitator, promoting localized oxygen transfer and redox reactivity [43,44]. Similar synergistic effects of Mg (and Al) as energetic additives and oxidation promoters have been reported in other thermite and reactive composite systems, as well as in Mg-containing redox active materials such as NiCo₂Oₓ for oxidation reactions [45].

The microstructural observations discussed above can be rationalized by considering the thermodynamic and kinetic role of Mg in the Fe/CuO system. Magnesium, the most reactive metal in the mixture ($\Delta H_{ox}(MgO) = 601.6$ kJ mol⁻¹), induces an ignition assisting mechanism that proceeds in three successive stages:

**Step 1: Mg initiated pre-ignition redox activation.**

Owing to its strong oxygen affinity and relatively low activation temperature, magnesium initiates its reaction with CuO early in the heating process. According to Chunmiao et al. (2013), Mg ignites within the range of approximately 450–600 °C, significantly lower than iron, whose oxide formation typically occurs between 900 and 1200 °C as reported by Chang (2025). This temperature difference enables Mg to ignite first, providing localized thermal spikes that initiate the thermite reaction front [46–48]:

$$Mg + CuO \rightarrow MgO + Cu \quad (11)$$

This highly exothermic reaction generates localized heat bursts that promote the formation of molten Cu and initiate the reduction of CuO even before the Fe driven thermite reaction begins.

**Step 2: Activation and propagation of the Fe/CuO thermite front.**

Once the local temperature exceeds the melting point of Cu (1085 °C), molten Cu is formed and enhances interfacial contact and heat transfer. This triggers the classical Fe driven thermite reaction:

$$3Fe + 4CuO \rightarrow 3FeO + 4Cu \quad (12)$$

The presence of liquid Cu accelerates oxygen transport and improves reaction front connectivity, leading to more stable and continuous combustion. This synergistic thermos chemical coupling between Mg induced heat release and Fe/CuO thermite kinetics is consistent with previous reports on multi fuel thermite systems [6,49].

**Step 3: Interfacial phase formation and microstructural consolidation.**

Post reaction SEM/EDS analysis reveals well defined metallic Cu regions, Fe rich oxide domains, and MgO particles preferentially dispersed at the Cu/FexOy interfaces. The accumulation of MgO at these boundaries suggests enhanced interfacial oxygen transfer and reactive wetting, which collectively promote improved densification and affect residual porosity. In certain areas, EDS mapping also reveals signatures of Fe/Cu interdiffusion and possible Fe-Mg-O mixed oxide phases, indicating limited alloying and solid-state diffusion processes at high temperature. These microstructural features are consistent with previous reports on Mg enhanced reactive composites [49].

These findings confirm that Mg serves simultaneously as an ignition promoter, heat amplifier, and diffusion facilitator, improving both ignition sensitivity and the extent of reaction. In future work, a detailed quantitative phase analysis using X ray diffraction (Rietveld method)

will be carried out as part of an ongoing collaborative study, in order to further elucidate the reaction mechanisms and confirm the phase composition of the combustion products.

## 5. Conclusion

The present study provides a comprehensive analysis of the combustion behaviour of Fe/CuO thermites compacted at 288 MPa, with particular emphasis on the effects of iron particle size distribution (PSD), Fe/CuO ratio, and the addition of 2.5 wt% Mg. The results show that the combustion front velocity is jointly controlled by the fuel oxidizer balance and the structural characteristics of the mixture. Burning rates increase with Fe content up to compositions close to the stoichiometric ratio, while excess iron reduces thermal feedback and slows reaction propagation. Particle size exerts a strong influence: fine Fe powders ($D < 20$ µm) promote faster and more stable fronts than intermediate and coarse fractions because of their larger specific surface and improved reactivity.

Mass variation measurements conducted on Mg free pellets indicate that mass loss or gain depends primarily on Fe concentration. Mixtures near 50 wt% Fe exhibit minimal mass variation, whereas Fe rich compositions show measurable mass gain attributed to post combustion oxidation in ambient air. Combined with initial porosity measurements, these results confirm that increasing Fe content leads to stronger structural densification during and after combustion.

SEM-EDS analyses identify the expected redox products metallic Cu and iron oxides (FexOy) and reveal that the post reaction porosity arises from the interplay between initial interparticle voids, thermomechanical shrinkage during oxidation, and localized melting phenomena. In CuO rich formulations, local deviations from the nominal Fe/CuO ratio may lead to transient oxygen release when Fe becomes saturated, consistent with the formation of larger cavities observed in the microstructures. These observations highlight the strong coupling between chemical redox pathways and mechanical deformation during combustion.

The addition of Mg significantly enhances reactivity across all PSD classes. The higher burning rates and the suppression of extinction events are consistent with the large exothermicity of Mg oxidation and its ability to initiate early-stage redox reactions. SEM-EDS mapping shows that MgO forms preferentially at Cu/FexOy interfaces, suggesting that Mg promotes oxygen transfer and contributes to the stabilization of the propagating front. In CuO rich systems, Mg addition also results in more extensive structural reorganization, consistent with locally higher reaction temperatures.

Overall, this study demonstrates that Fe/CuO thermite reactivity is governed by the combined influence of PSD, Fe/CuO ratio, intrinsic porosity, and Mg addition. These parameters control not only the burning rate and mass variation but also the nature of the redox pathways and the formation of post combustion porosity. The work provides an integrated experimental picture of the mechanisms shaping combustion in Fe/CuO thermites and establishes a framework for interpreting the interplay between chemical transformation and microstructural evolution.

### CRediT authorship contribution statement

**Nabil Mokrani:** Writing – original draft, Supervision, Methodology, Investigation, Formal analysis, Data curation. **Davney Ondzié-Pandzou:** Investigation. **Stéphane Bernard:** Methodology, Data curation. **Jean-Claude Harge:** **Léo Courty:** Writing – review & editing, Supervision, Project administration, Funding acquisition, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence
the work reported in this paper.

## Data availability

Data will be made available on request.

## References

[1] Teipel U. Energetic Materials 2004. https://doi.org/10.1002/3527603921.

[2] Jai Prakash Agrawal. High Energy Materials; 2015.

[3] Ketogenet T, et al. The effect of CuO on the thermal behavior and combustion features of pyrotechnic compositions with AN/MgAl. Sustain 2024;16(4):1-14. https://doi.org/10.3390/su16041488.

[4] Guidotti RA. Development history of Fe / KCIO heat powders at Sandia and related aging issues for thermal batteries; 2001.

[5] Panahi A, et al. Combustion behavior of single iron particles-part I: an experimental study in a drop-tube furnace under high heating rates and high temperatures. Appl Energy Combust Sci 2023;13(October). https://doi.org/10.1016/j.jaecs.2022.100097.

[6] Hosseini SG, Sheikhpour A, Keshavarz MH, Tavangar S. The effect of metal oxide particle size on the thermal behavior and ignition kinetic of Mg-CuO thermite mixture. Thermochim Acta 2016;626:1-8. https://doi.org/10.1016/j.tca.2016.01.005.

[7] Tekumalla S, Gupta M. An insight into ignition factors and mechanisms of magnesium based materials: a review. Mater Des 2017;113:84-98. https://doi.org/10.1016/j.matdes.2016.09.103.

[8] Tribelhorn MJ, Blenkinsop MG, Brown ME. Combustion of some iron-fuelled binary pyrotechnic systems. Thermochim Acta 1995;256(2):291-307. https://doi.org/10.1016/0040-6031(94)02190-Y.

[9] Gerlich MM, Wojewódka AT. Study of gasless compositions used in time-delay elements: Fe/BaO2 composition. J Therm Anal Calorim 2020;139(6):3473-9. https://doi.org/10.1007/s10973-019-08721-8.

[10] Panahi A, et al. Combustion behavior of single iron particles-part I: an experimental study in a drop-tube furnace under high heating rates and high temperatures. Appl Energy Combust Sci 2023;13(November). https://doi.org/10.1016/j.jaecs.2022.100097.

[11] Annesini MC, et al. Reduction kinetics of CuO-ZnO. Solid State Ion 1993;63-65: 281-8. https://doi.org/10.1016/0167-2738(93)90117-1.

[12] Polis M, et al. Ti/CuO and Ti/CuO/cellulose nitrate nanothermites: an early insight into their combustion mechanism. Energies 2024;17(17):1-51. https://doi.org/10.3390/en17174333.

[13] Liu JW et al. Thermal analysis and pyrolytic behavior of bimetal and double oxidant thermite Al/Mg/MoO3/CuO. Propellants Explos Pyrotech 2023;48(3). doi: 10.1002/prep.202200290.

[14] Stamatis D, Wainwright ER, Vummiid Lakshman S, Kessler MS, Weihs TP. Combustion of explosively dispersed Al-Mg-Zr composite particles. Combust Flame 2020;217:93-102. https://doi.org/10.1016/j.combustflame.2020.03.012.

[15] Fathollahi M, Pourmortazavi SM, Hosseini SG. The effect of the particle size of potassium chlorate in pyrotechnic compositions. Combust Flame 2004;138(3): 304-6. https://doi.org/10.1016/j.combustflame.2004.06.001.

[16] Gao H, Liu J, Xu P, Wang H, Fan J. Effects of Li content and particle size on the thermal decomposition and combustion characteristics of Al-Li alloys. Fuel 2025; 397:135368. https://doi.org/10.1016/j.fuel.2025.135368.

[17] Yue S et al. Agglomerate size evolution in solid propellant combustion under high pressure. Aerospace 2023;10(6). doi: 10.3390/aerospace10060515.

[18] Wang H, DeLisio JB, Jian G, Zhou W, Zachariah MR. Electrospray formation and combustion characteristics of iodine-containing Al/CuO nanothermite microparticles. Combust Flame 2015;162(7):2823-9. https://doi.org/10.1016/j.combustflame.2015.04.005.

[19] Kurt A, Davies TJ. A study of compaction of metal powders. Ulus Toz Met Konf Natl Powder Metall Conf 1996:493-506.

[20] Fathollahi M, Pourmortazavi SM, Hosseini SG. Particle size effects on thermal decomposition of energetic material. J Energ Mater 2008;26(1):52-69. https://doi.org/10.1080/07370650701719295.

[21] Rosêres C, Courty L, Gillard P, Boulnois C. Burning velocities of pyrotechnic compositions: effects of composition and granulometry. Energies 2022;15(11): 1-10. https://doi.org/10.3390/en15113942.

[22] Zapata J, Nicollet A, Julien B, Lahiner G, Esteve A, Rossi C. Self-propagating combustion of sputter-deposited Al/CuO nanolaminates. Combust Flame 2019; 205:389-96. https://doi.org/10.1016/j.combustflame.2019.04.031.

[23] Wang J, Yang H, Cheng L, Gao P, Li Y, Song D. Ignition and combustion characteristics of B/NC/CuO thermite microparticles. Metals (Basel) 2022;12(9): 1-12. https://doi.org/10.3390/met12091419.

[24] Tichtchenko E, et al. Numerical modeling and experimental study of self-propagating flame fronts in Al/CuO thermite reactions. Int J Therm Sci 2025;211. https://doi.org/10.1016/j.ijthermalsci.2025.109687.

[25] Tichtchenko E et al. Comprehending the influence of the particle size and stoichiometry on Al/CuO thermite combustion in close bomb: a theoretical study; 2023. doi: 10.1002/prep.202200334.

[26] Julien B, et al. Effect of substrate-induced localized stress on the combustion properties of Al/CuO reactive multilayer films. Thin Solid Films 2021;740:139000. https://doi.org/10.1016/j.tsf.2021.139000.

[27] Fischer S, Grubelich M. Theoretical energy release of thermites, intermetallics, and combustible metals. In: 24th Int. Pyrotech. Semin. 220(3):56:1998, [Online]. Available: http://journals.pepublishing.com/openurl.asp?genre=article&id=doi:10.1243/09544097F01505.

[28] Grapes MD, Reeves RV, Fezzaa K, Sun T, Densmore JM, Sullivan KT. In situ observations of reacting Al/Fe₂O₃ thermite: relating dynamic particle size to macroscopic burn time. Combust Flame 2019;201:252-63. https://doi.org/10.1016/j.combustflame.2018.12.021.

[29] Cabrera N, Mott NF. Theory of the oxidation of metals. Reports Prog Phys 1949;12(1):163-84. https://doi.org/10.1088/0034-4885/12/1/308.

[30] Zhang X, Song Y, Xiong X, Li Z, Yang W, Liu H. A new insight into surface oxidation of Fe-based metallic glass for azo dye degradation. J Water Process Eng 2025;76: 108170. https://doi.org/10.1016/j.jwpe.2025.108170.

[31] Ilunga K, del Fabbro O, Yapi L, Focke WW. The effect of Si-Bi2O3 on the ignition of the Al-CuO thermite. Powder Technol 2011;205(1-3):97-102. https://doi.org/10.1016/j.powtec.2010.08.071.

[32] Knapp S, Weiser V, Kelzenberg S, Eisenreich N. Modelling ignition and thermal wave progression in binary granular pyrotechnic compositions. Fraunhofer Inst. für Chem. Technol. ICT, 2014, [Online]. Available: sebastian.knapp@ict.fraunhofer.de.

[33] Bockmon BS, Pantoya ML, Son SF, Asay BW, Mang JT. Combustion velocities and propagation mechanisms of metastable interstitial composites. J Appl Phys 2005; 98(6):2-9. https://doi.org/10.1063/1.2058175.

[34] Brotman S, Djafari Rouhani M, Charlot S, Esteve A, Rossi C. A benchmark study of burning rate of selected thermites through an original gasless theoretical model. Appl Sci 2021;11(14). doi: 10.3390/app1146553.

[35] Weismiller MR, Malchi JY, Yetter RA, Foley TJ. Dependence of flame propagation on pressure and pressurizing gas for an Al/CuO nanoscale thermite. Proc Combust Inst 2009;32:1895-903. https://doi.org/10.1016/j.proci.2008.06.191.

[36] Saceleanu F, Idir M, Chaumeix N, Wen JZ. Combustion characteristics of physically mixed 40 nm aluminum/copper oxide nanothermites using laser ignition. Front Chem 2018;6:1-10. https://doi.org/10.3389/fchem.2018.004665.

[37] Shi K, Wang Y, Paul GI, Zachariah MR. The influence of heat feedback and thermal conductivity on the burn rate of thermite composites. Combust Flame 2024;vol. 269:113593. https://doi.org/10.1016/j.combustflame.2024.113593.

[38] ai Wang C, et al. Thermodynamics and performance of Al/CuO nanothermite with different storage time. Def Technol 2021;17(3):741-7. https://doi.org/10.1016/j dt.2020.05.003.

[39] Collins E, Pantoya M, Vijayasai A, Dallas T. Comparison of engineered nanocoatings on the combustion of aluminum and copper oxide nanothermites. Surf Coatings Technol 2013;215(September). https://doi.org/10.1016/j. surfcoat.2012.07.094.

[40] Choisez L, Van Ende M, Bruyr Z, Contino F, Pascal J. Influence of impurities on the use of Fe-based powder as sustainable fuel; 2025. doi: 10.1098/rsta.2023.0236/ 1329776/rsta.2023.0236.pdf.

[41] Ning D, Shoshin Y, Van Oijen J, Finotello G, De Goey P. Size evolution during laser-ignited single iron particle combustion. Proc Combust Inst 2023;39(3):3561-71. https://doi.org/10.1016/j.proci.2022.07.030.

[42] Hu W, Donat F, Scott SA, Dennis JS. RSC advances the interaction between CuO and Al₂O₃ and the reactivity of copper aluminates below 1000 C and their implication on the use of the Cu-Al-O system for oxygen storage and production †. RSC Adv 2016;6(1):113016-24. https://doi.org/10.1039/C6RA22712K.

[43] Wang H, Kline DJ, Biswas P, Zachariah MR. Connecting agglomeration and burn rate in a thermite reaction: role of oxidizer morphology. Combust Flame 2021;231: 111492. https://doi.org/10.1016/j.combustflame.2021.111492.

[44] Li C, Kang X. Effects of oxidizer structure on thermal and combustion behavior of Fe₂O₃/Zr thermite. Mater Res Express 2021;8(10). doi: 10.1088/2053-1591/ ac3040.

[45] Wang J, Chen Z, Cao T, Yang J, Kuang Y, Kang J. The effect of adding different elements (Mg, Fe, Cu, and Ce) on the properties of NiCo2OX for CO-catalyzed oxidation. Materials (Basel) 2025;18(11):1-16. https://doi.org/10.3390/ ma18112554.

[46] Chunmiao Y, Dezheng H, Chang L, Gang L. Ignition behavior of magnesium powder layers on a plate heated at constant temperature. J Hazard Mater 2013;246-247: 283-90. https://doi.org/10.1016/j.jhazmat.2012.12.038.

[47] Chang D. An experimental study on the ignition temperature of iron particles in an electrically-heated drop-tube furnace. An experimental study on the ignition temperature of iron particles in an 2025, doi: 10.1016/j.fuel.2025.136199.

[48] Drezin EL. Metal-based reactive nanomaterials. Prog Energy Combust Sci 2009;35(2):141-67. https://doi.org/10.1016/j.pecs.2008.09.001.

[49] Liu J et al. Thermal analysis and pyrolytic behavior of bimetal and double oxidant thermite Al/Mg/MoO₃/CuO 2023. doi: 10.1002/prep.202200290.