Introduction

Metal-based energetic materials are used in many applications such as termites [1, 2], energy storage, and pyrotechnics and explosives [3]. Light metal powders such as aluminum, magnesium and titanium can be added as high energy components to solid fuel or used as a metal suspension in hydrocarbon fuel [4]. Thermodynamic calculations indicate that the enthalpy of oxidation process of these metal-based energetic materials is higher than that of the hydrocarbon fuels [4, 5]. Among these metals, Aluminum powder is known as the most common metal additive due to its unique properties such as high enthalpy of its oxidation and relatively low cost [6,7,8].

The effect of oxidizing atmosphere [9,10,11], particle size [12], and heating rate [8] on the oxidation of aluminum powders has been investigated by researchers. Zhu et al. [10] studied the oxidation of aluminum powder in CO2 and CO2/O2 mixed oxidizers. They showed that the main characteristic of oxidation of aluminum powder in CO2 environment compared with that of O2 was the broadening of the γ-Al2O3 to α-Al2O3 phase transformation, so that it leads to fuller oxidation in CO2 environment. Also, the kinetics of the oxidation process of aluminum powder in the temperature range of 1000–1150 °C was performed in previous publications [13,14,15]. It is shown that the oxidation of these particles as a multi-step reaction is controlled by the Avrami–Erofeev model and the values of activation energies were calculated equal to 150–160 kJ/mol [13]. However, it has been accepted that oxidation of the aluminum powder particles is not completed even up to 1400 °C due to the presence of a protective oxide layer [14,15,16,17].

Magnesium powder particles are known as a high energy material, which can be oxidized without the presence of a protective oxide layer [18, 19]. Chunmiao et al. [11] showed that the non-isothermal magnesium powder oxidation under air atmosphere occurs in three stages. Although combustion enthalpy of the Mg powder particles is lower than that of the aluminum powder [20, 21], magnesium powder has a higher burning rate [22] with lower ignition temperature [21], which has attracted the attention of many researchers [5, 11, 23, 24]. Hence, they have focused on Al-based alloy powders such as Al–Mg, Al–Ti, and Al–Li to reduce the combustion delay [25, 26], and to increase burn rate [21, 27], and thermal efficiency [28, 29]. On the other hand, mixing metal powders can also be as another effective method [30,31,32], while the oxidation mechanism of these materials has not attracted much attention of researchers.

Therefore, in the present study, the oxidation mechanism of Al–Mg powder mixture is investigated. For this purpose, the kinetic parameters including activation energy (E), pre-exponential factor (A), and reaction model (g(α)) were calculated by using the isoconversional methods (Starink [33, 34] and FR [35] methods) in combination with invariant kinetic parameter (IKP) [36] and fitting [37, 38] methods.

Materials and methods

Materials and testing process

The powder mixture of Al50–Mg50 (in weight percentage) was prepared using the materials listed in Table 1.

Table 1 The specifications of the raw materials
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To characterize the chemical composition of the used commercial magnesium powder, the coupled plasma optical spectroscopy (ICP-OS) technique was employed and the results are listed in Table 2.

Table 2 Chemical composition of the Mg powder used in this study (measured by ICP-OS)
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To prepare the powder mixture, the reagents are mixed in a can by mini gearbox engine (Ming Jong Electric Co.) for 6 h with a speed of 4 rpm. Thermogravimetry (TGA) and differential scanning calorimetry (DSC) techniques were used by a Simultaneous Thermal Analysis (STA) device (NETZSCH STA 409 PC/PG) at various heating rates of 5, 10, 20, and 30 °C/min up to 1200 °C. The DSC/TGA analysis was carried out on approximately 25 mg quantities of powder mixture samples with sensitivity of ± 10 μW under air flow supplied at the rate of 30 mL/min. Based on the DSC/TGA curves, the characteristics temperatures of the oxidation process were determined.

For a detailed understanding of the oxidation process, the mixture powder samples were heated at a heating rate of 20 °C/min under air atmosphere up to the characteristics temperatures determined by DSC/TGA curves (500, 750, and 1000 °C). Then, these samples were subjected to phase analysis by using X-ray diffraction (XRD, Philips PW1730) with a Cu target (Cu Kα, λ = 0.15418 nm) radiation generated at a voltage of 40 kV and current of 30 mA. The samples were scanned in an interval of 10° < θ < 90° and at a scanning rate 1°/min with a step size of 0.05° in a continuous mode. XRD analysis of the investigated samples was performed using X’pert High Score software (3.0.5) in comparison with the reference powder diffraction data given by the Joint Committee on Powder Diffraction Standards (JCPDS). Also, microstructural observations were performed by using a scanning electron microscope (SEM, FEI ESEM QUANTA 200). The samples were gold coated for 240 s in a sputter coater in an Ar atmosphere before loading in SEM. The electrons at 20 kV sources were used to develop relevant information about the samples. The semiquantitative chemical analysis was carried out by energy-dispersive x-ray spectrometry (EDX, EDAX EDS Silicon Drift 2017), coupled to the scanning electron microscope.

Kinetic analysis

The values of the degree of conversion (α) at any given temperature and heating rate were calculated by using the peaks of DSC curves as follows [39]:

$$ \alpha = \frac{{A_{x} }}{{A_{\infty } }} $$
(1)

Here Ax is the peak area from the start temperature of reaction to a specified temperature (T) and A∞ is the total peak area.

To perform a comprehensive kinetic analysis, the isoconversional methods in combination with the fitting models are used [38,39,40,41,42,43,44]. Therefore, the kinetics of oxidation of powder mixture has been investigated by these methods.

Isoconversional methods

The isoconversional methods are used to obtain activation energy (E) and its dependence on α regardless of the reaction model, [38, 45, 46]. Among these methods, Starink and FR can be used to calculate more accurate values of E [47].

The integral Starink [33, 34] and differential FR [35] isoconversional methods are based on Eqs. 2 and 3, respectively:

$$\ln \frac{\beta }{{T^{{1.92}} }} = {\text{const}}. - 1.0008\frac{E}{{RT}} $$
(2)
$$ \ln \left[ {\beta \left( {\frac{d\alpha }{{dT}}} \right)} \right] = \ln \left[ {Af(\alpha )} \right] - \frac{E}{RT} $$
(3)

Here α is the degree of conversion, β is the linear heating rate (°C/min), T is the absolute temperature (K), R is the general gas constant (J/mol K), and E is the activation energy (kJ/mol).

For α = const., the E values can be evaluated from the slope of the plots of ln(β/T1.92) vs. 1/T and ln[β (dα/dT)] vs.1/T without knowing the reaction model.

Invariant kinetic parameter (IKP) method

In this method, invariant kinetic parameter including Einv and Ainv values are obtained with the intersection of lnA versus E curves in an appropriate kinetic model [36]. For this purpose, the values of Eg(α) and lnAg(α) are achieved for all heating rates and algebraic expressions (g(α)) (which have been presented in the previous publications [38, 40, 48]) by using the Coats-Redfern (CR) [49] method (Eq. 4).

$$ \ln \frac{g(\alpha )}{{T^{2} }} \cong \ln \frac{AR}{{\beta E}} - \frac{E}{RT} $$
(4)

According to IKP method, there is a linear relationship between the values of E and lnA at each heating rate (Eq. 5). So, the lines drawn at various heating rates intersect at a given point, if there is a constant mechanism. This intersection represents values of Einv and lnAinv for the correct reaction model [36].

$$ \ln A_{i} = a + bE_{i} $$
(5)

In Eq. 5, subscript ‘‘i’’ represents the heating rate; a and b are the compensation effect parameters.

Fitting models

As mentioned, the isoconversional methods determine the activation energy without determining the reaction model and the pre-exponential factor. Therefore, the fitting models are used not only to validate the results obtained by isoconversional and IKP methods but also to determine two other kinetic parameters [37, 38]. According to the fitting model, the reaction model is specified by plotting experimental and theoretical data of g(α) and obtain the best matching between them. The theoretical curves of g(α) as a function of α can be plotted by using the algebraic expressions for g(α), which have been indicated in the previous literature [38,39,40, 48]. The experimental curves of g(α) as a function of α can be plotted by using the following Eq. 6.

$$g(\alpha ) = \frac{A}{\beta }\int_{0}^{T} {\exp \left( { - \frac{E}{{RT}}} \right)dT} $$
(6)

Here the temperature integral in Eq. 6\(\int_{0}^{T} {\exp ( - \frac{E}{RT})dT}\) is determined by Eq. 7 [50];

$$ \int_{0}^{T} {\exp \left( { - \frac{E}{RT}} \right)dT = \frac{{RT^{2} }}{E + 2RT}\exp \left( { - \frac{E}{RT}} \right)} $$
(7)

Results and discussion

Thermal analysis

Fig. 1 displays the DSC and TGA curves of the Al–Mg powder mixture. As shown, there are two exothermic peaks at different heating rates, corresponding to the extreme weight gain in the TG curves. Thus, the oxidation process of the powder mixture is carried out in two steps. On the other hand, it is shown that the oxidation steps shift to higher temperatures with an increase in heating rate, which can be attributed to thermally activated process [51,52,53,54]. These results are in a good agreement with other thermally activated processes [55, 56].

Fig. 1
figure 1

a DSC and b TG plots of the oxidation of Al–Mg powder mixture at various heating rates under air atmosphere

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Fig. S1 illustrates the DSC curves related to the pure Mg and Al powders and Al–Mg powder mixture at a heating rate of 20 °C/min. By comparing the two DSC curves of magnesium powder particles (Fig. S1) and the powder mixture (Fig. 1a), it is illuminated that the first peak of the DSC curve of the powder mixture is related to the oxidation of magnesium powder particles in the powder mixture.

On the other hand, the DSC curve of Al powder particles (Fig. S1) represents an endothermic peak and an exothermic peak, which are related to the melting of aluminum at 660 °C and the partial oxidation of these particles at 1060 °C [13,14,15, 57]. Therefore, it is concluded that a small endothermic peak observed in the DSC curve of the Al–Mg powder mixture at a heating rate of 10 °C (Fig. 1a) can be related to the melting of Al (~ 660 °C). Moreover, previous publications [13, 14] showed that there is a great amount of residual aluminum in the pure Al powder particles heated up to 1200 °C. While, the DSC curve of Al–Mg mixture particles shows that aluminum powder particles in the Al–Mg powder mixture are oxidized at lower temperature (880 °C) compared to that of pure aluminum powder particles (1060 °C).

Phase analysis

The XRD patterns of the raw powder mixture and the samples annealed at a heating rate of 20 °C/min up to the selected temperatures in accordance with the DSC curves are shown in Fig. 2. As seen, only Al and Mg peaks (JCPDS card No. 001-1176 and 03-065-3365) are observed in the XRD patterns of both the raw sample and the sample annealed up to 500 °C, indicating that no oxidation occurs up to 500 °C, which is in agreement with the DSC curve.

Fig. 2
figure 2

XRD patterns related to the raw Al–Mg powder mixture and the samples annealed from ambient temperature up to various temperatures at a heating rate of 20 °C/min under air atmosphere

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With an increase in maximum temperature up to 750 °C, aluminum, magnesium oxide (MgO; JCPDS card No. 01-075-1525) and spinel (MgAl2O4; JCPDS card No. 01-075-1797) phases are identified in the XRD pattern. Therefore, it is confirmed that only the magnesium oxidation is carried out at the first peak of the DSC curves according to the following reaction [11]:

$$ {\text{Mg}}_{{{\text{(s)}}}} + \frac{{\text{1}}}{{\text{2}}}{\text{O}}_{{{\text{2(g)}}}} \to {\text{MgO}}_{{{\text{(s)}}}} {; \Delta {\rm G}}_{{577\,{^\circ {\rm C}}}} { = - 510 {\rm kJ}/{\rm mol}} $$
(8)

The presence of a protective oxide layer on the surface of aluminum particles delays their oxidation; therefore, this process does not start until the temperature reaches 800 °C. Nevertheless, it is observed that the oxidation of aluminum particles in the powder mixture begins at lower temperatures than in pure aluminum particles, which can be attributed to the reduction of the strength of the protective oxide layer as a result of the oxidation in the first stage.

It is reported that the expansion of the aluminum melt inside the crust can play a significant role to overcome the strength of the crust [15]. Thermal stresses caused by oxidation of the first stage cause the oxidation of aluminum particles in the second stage at lower temperatures. Therefore, this powder mixture can be considered as a solid fuel.

In the second stage of oxidation, the following two reactions is taken place by tearing the oxide shell [23]:

$$ 2{\text{Al}}_{{({\text{l}})}} + \frac{3}{2}{\text{O}}_{{2({\text{g}})}} \to {\text{Al}}_{2} {\text{O}}_{{3({\text{s}})}} ;\Delta {\text{G}}_{{877^\circ {\text{C}}}} = - 1314.8\;{\text{kJ}}/{\text{mol}} $$
(9)
$$ {\text{MgO}}_{{({\text{s}})}} + 2{\text{Al}}_{{({\text{l}})}} + \frac{3}{2}{\text{O}}_{{2({\text{g}})}} \to {\text{MgAl}}_{2} {\text{O}}_{{4({\text{s}})}} ;\Delta {\text{G}}_{{877^\circ {\text{C}}}} = - 1361.5\,{\rm kJ}/{\rm mol} $$
(10)

As shown in Fig. 2, XRD pattern of the sample annealed up to 1000 °C confirms the existence of spinel phase (MgAl2O4). Therefore, the second stage of oxidation of the powder mixture can be accompanied by the formation of MgAl2O4 (reaction (10)). This spinel phase (MgAl2O4) has a Pilling–Bedworth ratio greater than one (1.30) [23, 58], indicating that this phase can form a continuous oxide film on the surface of the remaining aluminum, which can prevent the remaining aluminum from oxidizing. Therefore, the aluminum peaks appear in XRD pattern of the sample annealed up to 1000 °C. The thermodynamic calculations of reactions (9) and (10) also show that the reaction (10) is preferable, which is in a good agreement with the obtained results.

Microstructural observation

Fig. S2 represents the SEM micrograph and EDS map of the raw powder mixture. Also, SEM micrograph and EDS map of the sample annealed up to 500 °C are shown in Fig. S3. As seen, no oxidation occurs in the powder mixture by heating up to 500 °C. In our previous publication [20], it was revealed that Mg(OH)2 with a Pilling–Bedworth ratio of 1.76 is formed as a thin continuous oxide layer on the surface of magnesium particles; therefore, this layer can prevent the oxidation of these particles up to ~ 500 °C. Therefore, no significant oxidation should be expected up to 500 °C, which is in accordance with the phase and microstructural analyses of the sample annealed up to 500 °C.

At temperatures above 500 °C, where Mg(OH)2 is unstable and converts to MgO with a Pilling–Bedworth ratio of 0.81, cannot serve as a barrier layer [20, 59]. Fig. S4 represents the SEM micrograph and EDS map of the sample annealed up to 750 °C. Unlike aluminum particles, magnesium particles are oxidized in this sample.

Fig. S5 shows the SEM micrograph and EDS analysis of the sample heated up to 1000 °C. As seen, the phenomena related to the oxidation of aluminum particles such as bursting of the protective shell of Al particles, oxidation of these particles, and the resulting agglomeration of the particles are well proven in this figure. The yellow arrow indicates the tearing of the alumina shell on the surface of the aluminum particles. Also, the stoichiometry of the formed phase and the theoretical one are compared in Table 3 to better understand the phase formed in this sample. As listed, the presence of the MgO and MgAl2O4 phases are confirmed in areas 1 and 2, respectively.

Table 3 Elemental composition of the phases formed in the sample heated up to 1000 °C as evaluated from the stoichiometry composition and EDS
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Kinetic analysis

Isoconversional methods

Fig. S6 displays the plots of α vs. T for the two steps of oxidation process of the powder mixture at various heating rates. The characteristic temperatures extracted from DSC/TGA curves are listed in Table 4.

Table 4 Kinetic parameters obtained by isoconversional, IKP, and fitting methods
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The plots of E vs. α are shown in Fig. 3. As seen, the activation energy calculated for the first peak is strongly dependent on α, while for the second peak, this dependence is less expressed (in the range of 0.1 ≤ α ≤ 0.9), indicating that there is no unique kinetic mechanism for each of these two oxidation steps. In other words, both stages are multi-step reactions.

Fig. 3
figure 3

The dependence of E on α evaluated for two oxidation steps of the oxidation of Al–Mg powder mixture under air atmosphere; calculated by isoconversional a Starink and b FR methods

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Also, the ranges of activation energy determined by both isoconversional methods are listed in Table 4. However, the values of activation energy evaluated by the Starink and Friedman methods are in good agreement with each other.

IKP method

The values of E and lnA for every kinetic model at each heating rate are obtained using the CR method (Eq. 4). Fig. 4 represents the linear relationship between E and lnA for both oxidation stages at various heating rates.

Fig. 4
figure 4

The compensation relationship and its enlarged region for the a first and b second oxidation stages of Al–Mg powder mixture under air atmosphere; calculated by IKP method

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As shown, these lines do not intersect at a given point, indicating that the certain E and lnA cannot be achieved. Hence, the results of isoconversional methods that both stages are multi-step reactions are confirmed by the IKP method.

Fitting models

The fitting method is used to determine the reaction model for both oxidation steps. Fig. 5 represents the theoretical and experimental g(α) vs. α curves for the first and the second steps of oxidation process of the powder mixture at various heating rates.

Fig. 5
figure 5

Plots of the experimental and theoretical g(α) vs. α for the a first and b second oxidation stages of Al–Mg powder mixture under air atmosphere

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The results obtained from these curves are reported in Table 4. As presented, these results are in a good agreement with that obtained by isoconversional and IKP methods. Also, for the first oxidation stage, it is seen that this stage is controlled by A2, R2, and D2 at the heating rates of 5, 10, and 30 °C/min. Moser et al. [5] performed a non-isothermal kinetic analysis on the oxidation of pure magnesium powder and showed that this process was controlled with A2 model at heating rates less than 5 °C/min. This model demonstrated that the oxidation is controlled by the nuclei growth rate of MgO that is proportional to two-dimensional diffusion [60].

At a heating rate of 10 °C/min, the reaction follows the R2 model. According to this model, nucleation occurs rapidly on the surface of the crystal and the reaction is controlled by the resulting reaction interface progressing towards the center [60].

At a heating rate of 30 °C/min, the D2 model (two-dimensional diffusional model) is determined for the reaction. At a high heating rate, the product formation rate (MgO) occurs relatively fast, which can lead to the concentration gradient of oxygen around the magnesium powders. Therefore, the diffusion of oxygen controls the reaction rate. Unlike the first stage of oxidation, in the second stage of oxidation, the reaction follows Avrami-Erofeev models at all three heating rates. This oxidation stage follows the A3 and A2 models at heating rates of 5 and 10 °C/min, respectively. However, the reaction model changes from A3 to A2 in α = 0.5 at a heating rate of 30 °C/min. Hence, the second step of oxidation is controlled by the nucleation and nuclei growth rate of MgAl2O4, so that the growth rate of nuclei is proportional to the interphase area [61, 62].

Conclusions

In the present research, non-isothermal kinetic analysis of the oxidation process in the Al–Mg powder mixture was investigated. According to DSC-TGA results, this oxidation process of the Al–Mg powder mixture was divided into two stages. Phase analysis revealed that only the magnesium powder particles were oxidized during the first step of the process. During the second oxidation step, the protective oxide layer on the surface of aluminum particles was broken and the spinel phase (MgAl2O4) was formed due to the contact of aluminum melt with the magnesium oxide (MgO) formed in the first step. Moreover, the obtained results revealed that aluminum powder particles in the powder mixture is oxidized at lower temperatures and more completely compared with pure aluminum powder. Furthermore, activation energy of two oxidation stages of the Al–Mg powder mixture was calculated by isoconversional Starink and Friedman methods. At both stages, the activation energy obtained decreased as the reaction progressed. IKP method also confirmed the results of the isoconversional method. Based on the results obtained by fitting method, the first oxidation stage was controlled by A2, R2, and D2 models at the heating rates of 5, 10 and 30 °C/min. In the second step, the reaction followed the A3 and A2 models at heating rates of 5 and 10 °C/min, respectively, and the reaction model changed from A3 to A2 at α = 0.50 at the heating rate of 30 °C/min.