oxygen gas mixtures

Journal of Hazardous Materials 260 (2013) 707–714

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Thermal analysis of magnesium reactions with nitrogen/oxygen gas mixtures Yuan Chunmiao a,∗ , Yu Lifu a , Li Chang a,b , Li Gang a , Zhong Shengjun a a b

Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110819, China Department of Civil Engineering, Shenyang Jianzhu University, Shenyang 110168, China

h i g h l i g h t s • • • •

Total oxidation and nitridation heat decreases linearly from 79% to 95% N2 in O2 /N2 mixture. Preference of oxidation was weakened by nitridation in higher N2 /O2 ratio mixture than air. Two growth stages of coating layer are identified in entire Mg oxidation/nitridation process. Activation energy can be derived from TG data for entire Mg oxidation instead of nitridation.

a r t i c l e

i n f o

Article history: Received 22 March 2013 Received in revised form 18 June 2013 Accepted 19 June 2013 Available online 27 June 2013 Keywords: Magnesium powder Oxidation Nitridation Thermogravimetric analysis Activation energy

a b s t r a c t The thermal behavior and kinetic parameters of magnesium powder subjected to a nitrogen-rich atmosphere was investigated in thermogravimetric (TG) and differential scanning calorimeter (DSC) experiments with oxygen/nitrogen mixtures heated at rates of 5, 10, 15, and 20 ◦ C/min. At higher temperature increase rates, the observed oxidation or nitridation steps shifted toward higher temperatures. The comparison of mass gain and heat of reaction in different nitrogen concentrations is helpful in interpreting the inerting effect of nitrogen on magnesium powder explosion in closed vessels. Activation energies for oxidation in air calculated by the Kissinger–Akahira–Sunose (KAS) method are generally consistent with previously published reports, but the method was not successful for the entire nitridation process. The change of activation energy with temperature was related to protective properties of the corresponding coating layer at particle surfaces. Two main coating layer growth processes were found in magnesium oxidation and nitridation using a modified Dreizin method which was also employed to determine activation energy for both magnesium oxidation and nitridation. For magnesium powder oxidation, activation energy calculated by the Dreizin method was close to that by KAS. Variation in activation energies was a function of different mechanisms inherent in the two methods. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Magnesium powder is widely used as a high energy density additive in propellants, pyrotechnics, and explosives [1]. Many researchers have reported its combustion characteristics [2–6] and oxidation mechanism [7–11] when used as a fuel. However, very fine magnesium dust has a minimum ignition energy (<2 mJ) as low as certain combustible gas mixtures and thus is considered a hazardous material [12,13]. Ultra-fine magnesium powder without an original oxide coat can spontaneously ignite even at room temperature in a stream of O2 /N2 [14]. In addition,

∗ Corresponding author at: Institute of Safety Engineering, Box 265, Northeastern University, Shenyang, Liaoning 110819, China. Tel.: +86 24 83681830l; fax: +86 24 83681483. E-mail address: [email protected] (Y. Chunmiao). 0304-3894/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jhazmat.2013.06.047

explosion venting technology is not effective for fine magnesium dust because of extremely high explosion severity [(dP/dt)max , Pmax ] [15]. For this reason, inerting technology was recommended as a means of magnesium dust explosion prevention [16–20], while similar investigations have been conducted with gas [13,21] or solid inertants [22,23]. The effectiveness of nitrogen as a low cost inertant for many flammable mixtures is well known. However, nitrogen likely would not provide explosion protection for powdered metals such as aluminum and magnesium [24] due to an exothermic chemical reaction between nitrogen and metal dust to form the corresponding nitrides [25–27]. Under such conditions, nitrogen becomes a reactive gas rather than an inerting agent. However, experimental results for magnesium clouds in a 20-L sphere indicated that nitrogen had an inerting effect similar to that of argon when the oxygen concentration of the inerted atmosphere was greater than 12.2% by volume [21]. Nifuku et al. [13] similarly found that minimum

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Y. Chunmiao et al. / Journal of Hazardous Materials 260 (2013) 707–714

Fig. 1. Mg powder particle size distribution (D50 = 6 ␮m, metal content 96.34%). Fig. 2. SEM image of Mg powder.

oxygen concentrations producing a dust explosion were about 8% by volume for magnesium with nitrogen as the dilutant. Thus, it seems that nitrogen may still have potential as an inerting agent. Studies on the nitride formation aspects of metal powders such as Al, Ti, and Zr [26–28] have indicated that the inerting effect of N2 may be caused by a nitridation reaction with significantly lower combustion enthalpy compared to an oxidation reaction. However, little information is available on the thermal behavior and reaction kinetics of Mg powder in a nitrogen rich atmosphere. Also lacking from the literature is a rational explanation for the inerting effect of nitrogen on magnesium powder explosion. Thermogravimetric analysis (TGA) is extensively used to determine thermal behavior and reaction kinetics. Several researchers [29–32] have applied the Arrhenius model to derive reaction constants and activation energies from TG/DTG thermograms. TGA can also be performed using both isothermal and non isothermal techniques which offer several advantages [33–36]. In this paper, TGA was employed to investigate the reaction characteristics of Mg powder under different nitrogen supply concentrations, and then to provide kinetic analysis. Different heating rates were used for the kinetic analysis to obtain apparent activation energy via the KAS method. Also, the Dreizin method was modified for estimating the activation energy of magnesium powder in air and nitrogen. Xray diffraction (XRD) was used to study the content of magnesium powder and its final reaction products in oxidation and nitridation. 2. Materials and methods TG and DSC experiments of magnesium powder oxidation and nitridation were performed in different O2 /N2 mixtures with heating rates of 5, 10, 15, and 20 ◦ C/min using a STA 449C (NETZSCH, German) thermogravimetric analyzer. Magnesium powder with a nominal size of 6 ␮m (particle size distribution is shown in Fig. 1) was loaded in an alumina sample pan. SEM imaging (Fig. 2) indicated a nearly spherical morphology. The percentage of active content of samples provided by Haowei Magnesium Powder Co., Ltd was 96.34% [37,38]. Fig. 3 shows an XRD diagram of magnesium powder samples. Apart from metallic magnesium, magnesium oxides were not the only compounds, with certain levels of magnesium hydroxide also detected. All instrumentation was calibrated according to the manufacturer’s recommendations. Non-isothermal oxidation and nitridation of the samples were performed in the thermobalance furnace under controlled temperature to obtain corresponding TG and DSC curves. For each heating rate, three replicate TG curves were obtained in order to assure reproducibility of results. Mg

Fig. 3. XRD pattern of magnesium powder.

samples of approximately 6–8 mg were placed in the TGA microbalance pan. This amount was sufficient to cover the bottom of the pan because of low sample density. Nitrogen and oxygen were used as purge gases. The atmosphere for all TGA/DSC experiments was a mixture of nitrogen and oxygen. The concentration of nitrogen was controlled by a mass flow valve built into the thermogravimeter. In all experiments, combined flow was adjusted to 20 mL/min, and samples were heated from ambient temperature (25 ◦ C) to 1000 ◦ C at the respective temperature increase rates. Residual weight of the sample and heat flux with respect to time and temperature were recorded using NETZSCH Proteus software. 3. Results and discussion 3.1. Validation of metal content of sample Data from TGA can be used to estimate or validate the oxide content of the tested powders [39]. The samples were heated under air or a pure nitrogen atmosphere from 25 to 1000 ◦ C. From about 800 to 1000 ◦ C, no obvious mass gain was observed in the two experimental conditions (Fig. 4), which may indicate that metal in the samples was almost completely consumed. The oxidation reaction I in air and nitridation reaction II in pure nitrogen for magnesium powder would be expressed as follows [40–42]: ReactionI : Mg(s) + 1/2O2 (g) → MgO(s) − 592.8 kJ

(1)

Y. Chunmiao et al. / Journal of Hazardous Materials 260 (2013) 707–714

709

170 165

Expected mass line of 167% for reaction I

160

Mass: 160%

150

150

5K 10K 15K 20K

Expected mass line of 139% for reaction II

130

Mass (%)

Mass (%)

140

Mass: 137%

120

Mass:98%

5 ºC/min, In Air 5 ºC/min, in Nitrogen

110

Mass:99%

135

III

II

Stage I

72% 69%

Melting point line: 70% ~ 75%

120

105

Initial mass line of 100%

100

Initial mass line of 100%

90

90 200

400

600

800

0

1000

200

Fig. 4. TGA of magnesium powder reacted in air and nitrogen atmosphere. Nominal heating rates are indicated.

mf − mo m × m0

800

1000

Fig. 5. TGA for magnesium powder oxidation at different heating rates in air.

III

II

165

0

(2) B

150

-50

Mass Mass (%)

The expected mass gains m were 67% and 39% for reactions I and II, respectively. The actual mass gain allowed evaluation of the metallic magnesium content of the sample, while the remaining main portion may have been magnesium oxide according to XRD analysis of magnesium powder samples (Fig. 3) and as expected when considering the presence of oxygen in the ambient air. The slight loss in mass below 500 ◦ C corresponded to evaporation of residual water and decomposition of magnesium hydroxide. Metal content in the sample can be calculated as follows: Mg (wt%) =

600

Temperature ( ºC)

Temperature ( C)

ReactionII : 3Mg(s) + N2 (g) → Mg3 N2 (s) − 462.8 kJ

400

DSC 135

120

Stage I

Melting point, 650 º C -100

I: 330~500 º C II: 500~610 º C III: 610~800 º C

Peak value: A: (590,-213) B: (752,-20)

105

-150

DSC (mW/mg)

0

-200

A

(3)

where m0 is the initial mass of the sample minus the mass loss mentioned above, and mf is the mass gain of reactions I and II, respectively. The curves of 5 ◦ C/min heating rate were employed for the calculation because the lower heating rate corresponded to a much longer heating time and a much slower process of oxidation or nitridation of the magnesium powder [43]. Calculated metal content of the sample was 94.4% for reaction I and 98.4% for reaction II. Both values approximate the 96.34% figure claimed by the manufacturer, and the relative errors are less than 3%. 3.2. Oxidation and nitridation of magnesium powders The TG curves in Fig. 5 show sample mass increase as a function of temperature for magnesium powder heated at different heating rates in air. At higher temperature increase rates, the observed oxidation steps shifted toward higher temperatures. Similar trends have also been observed for aluminum powder and certain organic compounds [29,31,43,44]. In Fig. 6, the TGA curve can be divided roughly into three regions pertaining to mass gain. These stages are shown schematically using a typical TG and DSC curve. The DSC curve is directly proportional to the rate of oxidation which is similar to the derivative of the TG curves [44,45]. The minus sign in the DSC curves indicates an exothermic reaction. Here, a heating rate of 5 ◦ C/min in air was selected as an example. During the first stage, magnesium hydroxide decomposed or residual water evaporated in the temperature range of about 330–500 ◦ C. Mass decreased by 1.7–3.1%, depending on heating rate (Fig. 5). The oxidation and nitridation (Eqs. (1) and (2)) may occur, but their contributions to mass gains in this stage were almost neglectable because of quite slow reaction rates in such

90

-250 0

200

400

600

800

1000

Temperature ( ºC) Fig. 6. Stages in oxidation of magnesium powder in air. Heating rate was 5 ◦ C/min.

lower temperatures and the presence of comparatively strong protective oxide film [46]. In stage II (most intensive stage), the sample ignited in the temperature range of 500–610 ◦ C as indicated by a sharp weight increase. The DSC curve reached its first peak value of −213 mV/mg at about 590 ◦ C, after which the increase in oxidation rate abruptly terminated when the temperature of about 610 ◦ C was reached. In this region, this high oxidation rate resulted in oxidation of about 69–72% of available magnesium. The most probable reactions may include reactions I and II (Eqs. (1) and (2)). Oxidation slowed significantly before the magnesium melting point of 650 ◦ C (Fig. 6). During the third stage, oxidation rate continuously increased over the temperature range of about 610–800 ◦ C. The second peak value of −20 mV/mg was reached at about 752 ◦ C. The part of heat from environment was absorbed by solid Mg powders for melting (Eq. (4)) in this stage, and subsequently liquid Mg reacted with oxygen (Eq. (5)) and nitrogen (Eq. (6)) in air. Nearly all the magnesium was oxidized by about 1000 ◦ C. In stages II and III, there seemed to be neglectable effects of nitrogen on Mg oxidation although nitridation accompanied the stages because the reaction of Mg with nitrogen in air was considerably slower than that with oxygen [46]. It may be the reason why the final mass gain in air was very close to the theoretical one for oxidation as discussed in Section 3.1. Similar TG/DSC curves and stages for nitridation of magnesium powder in nitrogen are shown in Figs. 7 and 8, along with other key parameters mentioned above. Mg(s) ↔ Mg(l) + 8.6 kJ

(4)

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5K 10K 15K 20K

Mass change(%)

130

Stage I

III

II

160

79% N2 (in Air) 85% N2 90% N2 95% N2 100% N2

150 140

120

Mass (%)

140

58-73 %

110

130 120 110

Initial mass line of 100% 100

100 90

90 0

200

400

600

800

0

1000

200

400

600

800

1000

Temperature ( º C)

Temperature(º C) Fig. 7. TGA for magnesium powder nitridation at different heating rates in nitrogen.

Mg(l) + 1/2O2 (g) → MgO(s) − 608.4 kJ

(5)

3Mg(l) + N2 (g) → Mg3 N2 (s) − 479.6 kJ

(6)

Fig. 9. TGA for magnesium powder oxidation and nitridation at different N2 concentrations and a heating rate of 10 ◦ C/min.

60

-250

55

Mass gain(%)

TGA curves for magnesium powders heated at different N2 concentrations are shown in Fig. 9 for a heating rate of 10 ◦ C/min. Except for pure N2 , the observed reaction steps were very similar to each other and consistently shifted toward higher temperatures at higher N2 concentrations. The trend of sample mass increase as a function of temperature in 85–95% (by vol.) N2 was nearly identical to that of air, implying that oxidation occurred more readily than nitridation and that oxygen was more reactive with magnesium powder than was nitrogen, as determined for other metallic powders [26]. The relationship of mass gain at the end of stage II in each curve with different N2 concentrations is shown in Fig. 10. Mass gain declined significantly with increased N2 concentration in the experimental gas mixture, especially when approaching pure nitrogen. Given the great difference of expected mass gain for reactions I and II mentioned above, the lower mass gain might indicate that more magnesium reacted with nitrogen at higher N2 concentrations at equivalent heating rates. Except for pure nitrogen, the DSC value at Peak A nearly maintained its higher level, and decreased slightly

50

Mass gain

-150

DSC Value at peak A DSC Value at peak B

45

-100

DSC (mW/mg)

-200

3.3. Effect of concentration of nitrogen in atmosphere

40 -50

35

0

30 75

80

85

90

95

100

N2 concentration(%) Fig. 10. Relationship of mass gain with N2 concentration.

with increased N2 concentration. The reaction heat decreased linearly with increased N2 concentration from 79% to 95% as shown in Fig. 11. The DSC value and heat of reaction decreased sharply when N2 concentration was close to 100%. SEM images of the final products in the two different gas mixtures were shown in Fig. 12. There was no appreciable distinction among these images. Apart

2

III

140

Stage I

28000

-2

Mass (%)

DSC

-6 120

110

I: 330~480 II: 480~600 III: 600~700

Peak value: A:(508,-14.7) B:(647,-14.5)

ºC ºC ºC

-8

DSC (mW/mg)

-4

-10 -12

20000

16000

12000

B 100

Heat of reaction (J/g)

24000

Mass

130

R-Square of the fitting line: 0.984

0

II

-14

A -16 0

200

400

600

800

1000

Temperature( ºC) Fig. 8. Stages in nitridation of magnesium powder in nitrogen. Heating rate was 5 ◦ C/min.

8000 75

80

85

90

95

100

N2 concentration (%) Fig. 11. Relationship of heat of reaction with N2 concentration.

Y. Chunmiao et al. / Journal of Hazardous Materials 260 (2013) 707–714

Fig. 12. SEM images of final products in four different gas mixtures (by vol.): (a) 21%O2 /79% N2 and (b) 10% O2 /90% N2 .

from nearly spherical final products, the holes in the coating layers and their fragments can also be found. This could indicate the breaking of coating layer would occur in the reaction process, and then may affect its protective properties against further oxidation or nitridation. According to XRD images shown in Fig. 13, in an air atmosphere, Mg was primarily transformed into MgO, while more and more Mg3 N2 became the Mg product in the 5% O2 /95% N2 mixture. The combination of Figs. 10–13 suggests that magnesium powder reacted with oxygen preferentially while varying degrees of nitridation occurred in the different continuous O2 /N2 streams. Higher N2 concentrations resulted in greater levels of nitridation. These results may help interpret the inerting effect of nitrogen for magnesium powder explosion in closed vessels such as a 20-L sphere [21]. When magnesium powder clouds ignited and oxygen in the atmosphere was gradually depleted, more and more magnesium reacted with the increasing concentrations of nitrogen in the vessel [25]. Given the much lower DSC peak value and heat of reaction for pure nitrogen shown in Figs. 10 and 11, the reaction of magnesium with N2 significantly reduced the combustion enthalpy in comparison with oxidation as previously reported [26]. It is well known that overpressure is greatly affected by expansion factors which bring about an increase in volume during combustion. Lower combustion enthalpy will lead to lower expansion factors followed by overpressure [47]. 3.4. Kinetic analysis 3.4.1. KAS methods Among mathematical solutions for calculating kinetic parameters, the KAS method is best suited to a model free approach [32,36], and was utilized in this study to evaluate the activation energy of

711

Fig. 13. XRD patterns of the final products in air (a) and a 5% O2 /95% N2 mixture (b).

magnesium powder during oxidation in air and nitridation in pure nitrogen. KAS equation [32]:



ln

ˇ T2



= ln

AR Ea − RT EG(˛)

(7)

where ˇ is the constant heating rate (ˇ = dT/dt), A is the preexponential factor, Ea is the activation energy, R is the gas constant, and T is the absolute temperature. G(˛) is the integrated form of the conversion dependence function. ˛ is the degree of conversion of the mass gain process for reactions I and II, and can be expressed as follows: mt − m0 ˛= (8) mf − m0 Here, mt is mass of the sample at time t. According to Eq. (7), a plot of ln(ˇ/T2 ) against 1/T should be a straight line for a given conversion value. From the slope of TG curves, we can estimate apparent activation energy at various conversions ˛. Figs. 14 and 15 show the representative plots for the main stage of weight gain in air and nitrogen, respectively. The relationship of activation energy calculated by KAS methods with conversion for oxidation and nitridation is shown in Figs. 16 and 17, respectively. For air, activation energy declined in a narrow range of 200–293 kJ/mol with a mean of 231 kJ/mol. The mean approximated previously reported values [48] with a range of 210–220 kJ/mol. For nitrogen, the derived activation energy and its corresponding R-square of the regression line for conversion range from 0.1 to 0.9 were shown in Table 1. The negative activation energies or quite lower R-squares for the conversion range from 0.5 to 0.9 indicate that the method was not so successful for the entire nitridation process [32,49]. However, the method can be used to estimate activation energies for a special part of

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Conversions: 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-11.0

Stage II

Stage III

-11.5

0.0013

0.0014

0.0015

Activation energy (kJ/mol)

-10.5

2

ln(β/T )

-10.0

90

0.0016

85

Average line: 77.56 kJ/mol 80

75

70 0.0

0.0017

0.1

1/T

Stage II

Stage III

2

ln(β/T )

-10.0

-10.5

Conversions: 0.1 0.2 0.3

-11.0

-11.5 0.0015

0.0016

0.0017

0.4 0.5 0.6

0.0018

0.7 0.8 0.9 0.0019

0.0020

1/T Fig. 15. Plots for determining activation energy of nitridation in nitrogen at different conversions.

the whole process (i.e., conversion range from 0.1 to 0.4) because the activation energies in this region fell into the narrow range of 74–90 kJ/mol and R-squares of the regression lines were comparatively high (i.e., >0.9). In Fig. 16, activation energy in stage III varied

Activation energy(kJ/mol)

300

280

0.3

0.4

α

Fig. 14. Plots for determining activation energy of oxidation in air at different conversions.

-9.5

0.2

Stage II

Stage III

Line A: Average in total Line B: Average in Stage II Line C: Average in Stage III

Fig. 17. Activation energy and conversion for nitridation.

significantly from 293 kJ/mol at conversion 0.8 to 200 kJ/mol at conversion 0.9. According to conversions at melting point in different heating rates (Fig. 5), the temperature corresponding to conversion 0.8 was slightly above the melting point. At this temperature, heat from the environment would be absorbed to melt the rest of the metal in the samples, followed by a consequent change of mechanical stress induced by metal melting, thereby resulting in breakdown of the oxide coating layer formed before reaching the melting point at the particle surface [50]. Thus, less heat was available for further oxidation and increases of mass gain, and led to a lower metal reactivity (or higher activation energy) at this conversion. After breaking of the oxide coating layer (some fragments or holes of the coating layer can be seen in Fig. 12) at higher temperature (e.g., at conversion 0.9 in Fig. 16), further oxidation between residual molten metal would occur and lead to subsequent increases of mass gain. The transition of TG curve between stages II and III may be due to the change of protective properties of coating layers and metal phase induced by metal melting. The higher activation energy at conversion 0.4 in Fig. 17 may have been induced by greater nitrogen diffusion resistance when a thicker coating layer was formed at higher temperature below the magnesium melting point. 3.4.2. Dreizin method During heterogeneous oxidation or nitridation of metallic particles in gas mixtures, the reaction rate is usually governed to a great extent by the protective properties of coating layer. In order to distinguish growth stages of coating layer during the whole magnesium powder oxidation or nitridation, and then to recover activation energy for each stage in which a simple diffusion-limited oxidation or nitridation model is assumed, the TG curves in air and nitrogen were analyzed separately using the Dreizin method [43,49]. This method assumes that oxidation or nitridation occurs

260

C

Table 1 Activation energies and correlation coefficient (R) derived from TG data in Fig. 15.

A: 234 kJ/mol 240

246kJ/mol

Conversion

B:231 kJ/mol

220

200 0.0

0.2

0.4

0.6

0.8

α Fig. 16. Activation energy and conversion for oxidation.

1.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

E (kJ/mol) 73.6 72.5 74.1 90.1 64.7 −95.8 −110.8 −85.4 87.3

R-square 0.92 0.94 0.99 0.96 −0.05 0.61 0.90 0.53 −0.23

Y. Chunmiao et al. / Journal of Hazardous Materials 260 (2013) 707–714

350

Activation energy(kJ/mol)

Y(TGA), a.u.

B (649, 246)

250 200

A (510, 192)

150

B (763,97) 100 50 0 -50 450

0.0012

0.0014

0.0016

0.0018

0.0020

Stage III

Stage II 500

0.0022

1/T

A (595,341)

Air N2

300

Oxidation nitridation

713

550

600

650

T(º C)

700

750

800

Fig. 19. Change of activation energy in magnesium oxidation and nitridation with increased temperatures.

Fig. 18. Processed TGA curves used to determine activation energy of magnesium oxidation and nitridation.

as a series of individual diffusion processes through a growing surface oxidation or nitridation layer in which the intermediate/final products are formed. The values of these process-specific activation energies can be obtained from the differential TG curves by the following equation [49]: Ea = ln CA − ln RT

 dm  dT



− ln(ˇ) − ln

1 rMg

−

1



= Y (TGA)

rshell

(9)

where CA is a combined constant depending on reaction stoichiometry, initial sample mass, and type of diffusing species. rMg and rshell are the radii of the magnesium core and oxidation or nitridation shell, respectively, and can be calculated by Eqs. (10) and (11).



3 rMg =

1+

 3 rshell

=

 mt /mo − 1 · −1 

1 −  1 − ·  





·

 r3  + 1 −  0

 mt /mo − 1 1+ · −1 

(10)

 ·

 r3  + 1 −  0 (11)

Here, r0 is the initial radius of magnesium particles (3 ␮m).  is the percentage of active magnesium in the powder (96.34%).  and  are introduced for convenience.  is equal to MgO /Mg for oxidation and Mg3 N2 /Mg for nitridation.  is equal to Mg /MgO for oxidation and 3 · Mg /Mg3 N2 for nitridation. Mg , MgO , and Mg3 N2 are the molar masses of magnesium, magnesium oxide, and magnesium nitride, respectively. Fig. 18 illustrates implementation of the processing described above, with TG curves at 5 ◦ C/min in air and nitrogen selected as examples. In general, a positive slope illustrates an increasing oxidation or nitridation rate. The slope of a line tangent to the curve at a given point corresponds to the respective activation energy at a certain temperature. Activation energy can be obtained by the derivative of curves plotted in Fig. 18 against 1/T, and is a function of temperature (Eq. (12)). Ea = R ·

dY (TGA) = f (T ) d(1/T )

(12)

Both oxidation and nitridation processes were described by a diauxie curve (Fig. 19). One peak is located in stage II, and another in stage III. Thus, the entire oxidation or nitridation process may consist of two main sub-procedures or growth stages of the coating layer where products are formed. Temperatures at which peak value was reached in Fig. 19 were slightly larger than corresponding

temperatures shown in Figs. 6 and 8. As mentioned in Section 3.2, Peaks A and B in Figs. 6 and 8 corresponded to the temperatures at which oxidation or nitridation rate reached their maximum values, after which the coating layer developed and rapidly became thicker. The thick coating layer then offered a greater oxygen or nitrogen diffusion resistance, resulting in a significant decrease in metal reactivity (higher activation energy) at Peaks A and B in Fig. 19. Activation energy decreased quickly after Peaks A and B (Fig. 18). Mechanical stresses may have resulted in breakdown of the protective film, thus restoring metal reactivity and initiating further growth of the coating layer [49,50]. The peak value is the effective activation energy of the so-called diffusion-limited oxidation or nitridation in its corresponding stage. When the entire oxidation process occurred in air, the mean activation energy was 219 kJ/mol which was an average of the first peak at 341 kJ/mol and the second peak at 97 kJ/mol, and which approximated the value of 234 kJ/mol determined by the KAS method. Comparing Eqs. (7) and (9), the variation in calculated activation energies for magnesium powder oxidation may be explained by different mechanisms involved in the two methods. For the Dreizin method, a shrinking core model was taken into consideration [44,49–51]. However, in the KAS method which is regarded as a “model free” approach by many researchers [29,31,35,36], activation energy is derived without assuming a precise reaction model, and no growth of the coating layer is taken into consideration [32,36]. For magnesium powder nitridation, a similar comparison of activation energy is not possible because only part of the activation energy is available by the KAS method. Thus, a comprehensive comparison between the two methods will require further study of activation energy calculations. 4. Conclusions The entire process of mass gain for magnesium powder oxidation and nitridation in an oxygen/nitrogen mixture can be divided into three stages. Based on mass gain during sample heating in air and pure N2 , the calculated sample metal contents were close to those provided by the manufacturer with <3% relative error. Higher N2 concentration in the gas mixture not only decreased the final mass gain, but also led to much lower DSC values and lower reaction heats because of the greater degree of nitridation. The calculated mean activation energy determined by KAS for magnesium oxidation in air was 234 kJ/mol, but the method was not suitable for the whole process of magnesium nitridation. The change of activation energy with temperature during magnesium oxidation

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