ISSN 10613862, International Journal of SelfPropagating HighTemperature Synthesis, 2015, Vol. 24, No. 1, pp. 21–28. © Allerton Press, Inc., 2015.
Influence of HighEnergy Ball Milling on Reaction Kinetics in the Ni–Al System: An Electrothermorgaphic Study1 A. A. Nepapusheva, K. G. Kirakosyanb, D. O. Moskovskikha, S. L. Kharatyanb, A. S. Rogacheva, c, and A. S. Mukasyana,d aCenter
of Functional Nanoceramics, National University of Science and Technology, Russia b Institute of Chemical Physics, National Academy of Sciences, Armenia cInstitute of Structural Macrokinetics and Materials Science, Russian Academy of Sciences, Russia d Department of Chemical and Biomolecular Engineering, University of Notre Dame, USA email:
[email protected],
[email protected] Received November 17, 2014
Abstract—A new electrothermographic method, viz. highspeed temperature scanning, was applied to kinetic studies of reactions taking place in the Ni–Al system, including those after mechanical activation in a planetary ball mill. Treatment of the temperature profiles taken at different heating rates in terms of the Kissinger–Akahira–Sunose (KAS) approximation gave activation energy E for nonactivated mixtures: E = 155 kJ/mol (for temperature range 650–850°C). But for mechanically activated mixtures, the characteristic points (reaction onset temperature, temperature of maximum reaction rate) were found to decrease with increasing heating rate, which makes the KAS method inapplicable to these compositions. It has been con cluded that mechanical treatment leads to significant changes in the reaction kinetics, possibly due to split ting the reaction route into two stages the first of which has very low activation energy. Keywords: heterogeneous hightemperature reaction, mechanical activation, kinetics, thermography, nickel aluminide DOI: 10.3103/S1061386215010082 1
INTRODUCTION
Ni–Al system. The results of the HSTS experiments are compared with those obtained by other tech niques.
A variety of engineering technologies involve chemical reactions under essentially nonisothermal hightemperature conditions. It has been reported that heating rates may have marked influence on dif ferent processes, including chemical kinetics and phase transformation mechanisms [1–5]. Thus it is understood that under high heating rates, the kinetics of interaction between the reactants may differ signif icantly as compared to the kinetic laws obtained in nearisothermal conditions. The problem becomes even more complicated in the conditions typical of various combustion and plasma syntheses or laser induced processes where the rate of temperature change reaches a value of 103–105 K/s. In many cases, the observed reaction rates appear to be greater than those obtained in isothermal conditions. There are a few techniques which allow monitoring the kinetics of chemical reactions under such conditions, including the socalled electrothermographic [6, 7] and electro thermalexplosion analyses [8, 9]. In this work, a new thermographic method based on the use of highspeed temperature scanner (HSTS) [10–13] was used to investigate the kinetics of chemical reactions in the
EXPERIMENTAL Experiments were conducted with commercially available powders of Al (ASD1, Russia, particle size T0, and it attaining a maximum value (Tmax) at temperature T* on the inert profile. Thus the differ ence (ΔT) between Tmax and T* defines a temperature change owing solely to the heat release in reaction. At some moment, electric current is switched off and the sample is allowed to cool down. Note that our approach is similar to that adopted in conventional DTA method. However, HSTS provides much higher heating rates (up to 104 K/min) which can be precisely governed by PCassisted controller of power supply. To determine kinetic parameters of the reaction, the obtained data were processed in terms of the so called isoconversion method suggested by Kissinger [14] that is well known in thermography. In this method, the activation energy is calculated based on DTA the shift of Tmax in the DTA curve as a function of heating rate Vh:
(
)
⎛ Vh ⎜ ln ⎜ T DTA ⎝ max
(
)
⎞ ⎟ = ln A − E ⎛ 1 ⎞ , ⎜ DTA ⎟ 2 ⎟ R ⎝Tmax ⎠ ⎠
(1)
DTA is the reac where Vh is the heating rate (K/min), Tmax tion temperature which corresponds to the position of the maximum peak on the DTA curve (K), A is some constant, E the effective activation energy of the pro cess, and R the universal gas constant. It should be noted that, in conventional DTA method, the differ ence between Tmax and T* is small, i.e. the prepro grammed temperature of the furnace is close to real temperature of the sample. Following this approach, it
(a)
(b) 5
1 2
3
4
7
6
Fig. 2. Samples used in experiments and overall view of the experimental setup: (a) metal envelopes containing reactive mixture and (b) reaction chamber and controller: 1 reactive mixture, 2 boat of Ni foil, 3 powder mixture in the Ni boat, 4 envelope with reactive mixture and thermocouple, 5 heated sample, 6 reaction chamber, and 7 PCassisted controller. INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS
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INFLUENCE OF HIGHENERGY BALL MILLING ON REACTION KINETICS T, °C
Heating part
Tmax
23
Cooling part
1200 Intensive exotherm
900
ΔT
T0 TIheating
600
T* 300
0
Stop heating
Tinert heating
8
4
12 t, s
16
24
20
Fig. 3. Typical “reactive” and “inert” temperature profiles with characteristic temperatures.
T, °C 0 min
1200 3 min
1000 800
1 min 2 min
4 min 5 min
600 400 200
0
4
8
12 t, s
16
20
Fig. 4. Reaction thermograms for different Ni–Al mixtures (Vh = 2600 deg/min). Indicated are durations τ of HEBM.
is also assumed (for conditions of rapid heating in DTA ≡ T* (Fig. 3). However, this HSTS setup) that Tmax temperature gap in the HSTS method (Vh = 10– 10 000 deg/min) may be significantly larger than in the conventional DTA/DSC technique (Vh = 1– 100 deg/min). This difference may influence the results of kinetics analysis, as it will be shown below. RESULTS AND DISCUSSION The typical temperature profiles obtained for dif ferent Ni–Al mixtures heated at a rate of 2600 K/min are given in Fig. 4. As is seen in Fig. 5, the reaction onset temperature (T0) decreases with increasing τ
(Fig. 5a). For nonactivated powders T0 = 730°C, which is above the melting point of Al, while for acti vated powders it gradually decreases down to ~300°C. These data are in good agreement with those obtained earlier by other experimental methods [15, 16]. The characteristic values of T* also gradually decrease (Fig. 5b). It is important that the T* values for the samples pressed from the particles activated for more than 1 min are below the melting point of Al, which indicates that maximum heat release in these systems is due solely to solidstate reactions. The overheating (ΔTmax = Tmax – T*) which characterizes the amount of energy released, first slightly increases with milling time reaching maximum at τ = 3 min and then
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NEPAPUSHEV et al. T0, °C 900 600
600
300
300
0
1
2
T *, °C 900
(a)
T0, °C 900
(a)
3
4
5
0
1500
3000
T *, °C 900
(b)
4500
6000
7500
6000
7500
6000
7500
(b)
600
600
300 300 0 0
1
2
ΔTmax, °C 800
3
4
5
(c)
1500
ΔTmax, °C 800
3000
4500 (c)
600 600 400 400 200 200 0 0
1
2
3 τ, min
4
1500
5
Fig. 5. Parameters of thermal explosion—T0 (a), T* (b), and ΔTmax (c)—as a function of τ (Vh = 2600 deg/min).
decreases (Fig. 5c). The former can be explained by a higher extent of conversion during thermal explosion due to intermixing of the reactants to a nano level dur ing HEBM, while the former effect is due to possible interaction between Ni and Al directly in the milling jar. Thus these experiments confirmed results obtained by relatively slow (up to 100 K/min) conventional DTA method that HEBM leads to significant decrease in T0 and that in mechanicallyinduced nanomixed structures the reaction may proceed to a significant extent at temperatures below the eutectics in the Ni– Al system. Dependencies of T0, T*, and ΔTmax on Vh for non activated mixtures are shown in Figs. 6a–6c. It can be seen that all three parameters increase with increasing Vh. Such a behavior of T0 and T* is typical of the exo
3000 4500 Vh, deg/min
Fig. 6. Parameters of thermal explosion in nonactivated Ni–Al mixtures—T0 (a), T* (b), and ΔTmax (c)—as a function of heating rate Vh.
thermic systems with high activation energies, while increase in ΔTmax can be explained by the fact that the onset reaction temperature is higher at higher preheat ing rate. Using Eq. (1) and the data presented in Fig. 6b we plotted (Fig. 7) the Arrheniustype dependence, i.e. ⎛ V ⎞ 1 , which was then used to obtain the ln ⎜ h 2 ⎟ = F * T ⎝ (T *) ⎠ value of apparent activation energy E for the reaction in nonactivated Ni–Al powders. For the temperature range 650–850°C (which is above the eutectic tem perature for the Ni–Al system) E was found to have a value of 155 kJ/mol. This value fits well to that obtained in [17] by DTA/TG method for chemically activated mixture (159 kJ/mol) for the temperature
( )
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INFLUENCE OF HIGHENERGY BALL MILLING ON REACTION KINETICS –ln(Vh,/T *2) 10 8 6
E = 37.0 kcal/mol = 155 kJ/mol
4 2 8.5
9.0
9.5 10.0 10.5 (1/T) × 104, K–1
11.0
Fig. 7. Determination of apparent activation energy E for nonactivated Ni–Al mixture.
interval 650–750°C and is lower than that obtained in [9] by electrothermal explosion method for nonacti vated Ni–Al mixture (∼200 kJ/mol for T = 850– 1000°C). This result again confirms the durability of our method. The above data can be also compared with the effective activation energy obtained in the combustion experiments with Ni–Al mixtures. According to [18], the temperature dependences of burning velocity for mixtures with fine Ni powder gave E = 75–76 kJ/mol for T > 1455°C (melting point of Ni) and E = 140 kJ/mol for T < 1455°C. Mixtures with coarse Ni particles (41– 73 μm) showed E = 134 kJ/mol in the temperature range 1200–1600°C. Thus, our data are in a satisfac tory agreement with the combustion data obtained below the melting point of Ni or in experiments with coarse Ni powders. Typical temperature profiles of reaction in mechanically activated mixture (τ = 3 min) at differ ent Vh are shown in Fig. 8. Statistical treatment of such T, °C 1000
25
curves also allowed us to plot the values of T0, T*, and ΔTmax as a function of Vh (Fig. 9). It can be seen that the T0 and T* values, being always below the eutectic temperature (639°C) for the system, decrease with increasing Vh and such behavior is different as compared to that of nonactivated mix tures. Moreover, formal application of Eq. (1) under conditions when T* decreases with increasing Vh leads to negative apparent activation energy for the system. These effects require a special discussion. The Kissinger–Akahira–Sunose (KAS) method belongs to socalled p(y)isoconversion approach which is applicable under the assumption that param eter y = E/RT Ⰷ 1 [19]. Briefly, assuming that the reac tion rate (η ) is the product of two functions, one depending solely on temperature T and the other one solely on extent of conversion η, we obtain: dη = f ( η )k ( T ). dt
(2)
The temperature dependent function is generally assumed to be of the Arrhenius type: E k = k 0 exp ⎛ – ⎞ . ⎝ RT⎠
(3)
From (2) and (3) it follows that dη E ln = – – ln f ( η ) + const. dt RT
(4)
In case of linear heating rates, V = dT/dt = const, we may rewrite (4) in the form: E – ln f ( η ) ln ⎛ dη V⎞ = – ⎝ dT ⎠ RT
(5)
and hence E can be determined form a slope of the d η – 1/T plot. ln V dT
( )
2600°/min 390°/min
780°/min
800 600
260°/min
400 200 0
20
40
60 t, s
80
100
120
Fig. 8. Typical temperature profiles of reaction in mechanically activated mixtures (τ = 3 min) at different Vh (indicated). INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS
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NEPAPUSHEV et al.
Assuming that y Ⰷ 1, the following approximation to (7) can be obtained:
(a)
T0, °C 900
exp ( – y. ) p ( y ) ≈ p k ( y ) = 2 y
600
(8)
The assumption y Ⰷ 1 seems reasonable because for the majority of solidstate reactions 15 < y < 60. By taking the logarithm of Eq. (6) and using (8) one may obtain:
300
η
0 T *, °C 900
3000
1500
4500 (b)
6000
dη = k 0 E + ln 1 – y . ln ln f 2 f(η) R Vy f
∫
7500
(9)
0
And at constant extent of conversion η, we have: E + C , ln V 2 = – 2 RT f Tf
600 300
3000
0 1500 ΔTmax, °C
4500
6000
7500
6000
7500
(c)
800 600 400 200 0
3000 4500 Vh, min
1500
Fig. 9. Parameters of thermal explosion—T0 (a), T* (b), and ΔTmax (c)—in activated (τ = 3 min) Ni–Al mixtures as a function of Vh.
With account of (3) and (2), we have: η
∫ 0
Tf
k E dη = 0 exp ⎛ – ⎞ dT ⎝ V RT⎠ f(η)
∫ 0
(6)
∞
k E exp ( – y ) = 0 dy, 2 VR y y
∫ f
where y = E/RT, yf = E/RTf, and Tf is the temperature at an equivalent (fixed) state of transformation. The temperature integral on the right side is the so called Arrhenius integral p(y): ∞
exp ( – y )
dy = p ( y ). ∫ y 2
yf
f
(7)
(10)
which is exactly the formula (1) described above. According to this equation, the ln(Tf2 /V) – 1/Tf plot should represent a straight line with a slope equal to E/R. Thus, the correct application of the KAS method is based on the following assumptions: (a) the reaction is onestage, (b) its rate depends on temperature accord ing to Arrhenius law (3), (c) y = E/RT Ⰷ 1; and (d) the sample is heated linearly at constant rate V (5). For nonactivated mixtures, E ≈ 155 kJ/mol and thus, for T ~ 1000 K, y = E/RT ~ 20, which fits the assumption used in the Kissinger approximation. However, it is known that mechanical treatment leads to a significant decrease in E and thus the accuracy of the method decreases, which may lead, taking also into account the error of T* measurements, to nega tive values of the activation energy. On the other hand, close inspection of Fig. 8 sug gests that the values of Tmax increase with increasing Vh. If we assume that at T = Tmax the full conversion (η = 1) is achieved in all experiments with activated samples, then we may use Tf = Tmax as a reference tem perature in Eq. (10). The plot based on such an assumption is shown in Fig. 10. It can be seen that with fitting accuracy of 95% we do have a straight line with a slope corresponding to E of about 83 kJ/mol. This value is twice less than that for the nonactivated mix ture (see Fig. 7) and close to the data obtained by other methods for activated Ni–Al mixtures [9, 16]. Note that in this case parameter y is about 10. In our previous work [20] it has been shown that nanosized precursors of the reaction product appear during the HEBM of Ni–Al mixtures; therefore, the reaction splits into two stages. Part of the mixture, fraction x, transforms into some highreactive nanoc rystalline phase (reaction precursor) and reacts with low activation energy E2; the rest fraction, 1 – x, retains initial reactivity and activation energy E1; E2 < E1. Then
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INFLUENCE OF HIGHENERGY BALL MILLING ON REACTION KINETICS
ACKNOWLEDGMENTS This work was supported by SCS RA and RFBR joint Armenian Russian research Grant AR 13RF 057 // 130390604. The authors also gratefully acknowledge the financial support of the Ministry of Education and Science of the Federation in the frame work of increase Competitiveness of NUST “MISIS” (No. K22014001).
–ln(V/Tmax2) 8
Equation Weight Residual sum of squares Pearson’s r Adj. RSquare D
27
y = a+ bx No weighting 0.26902 0.97104 0.9315 Value Standard error Intercept –2.49229 1.00228 Slope 11192.6646 1231.56047
7
REFERENCES 6
5 0.0007
0.0008 1/Tmax
0.0009
Fig. 10. Determination of apparent activation energy E for activated (τ = 3 min) Ni–Al mixtures.
the reaction rate (W) at temperature T can be repre sented in the form: W = ke
E eff RT
= ( 1 – x )k 1 e
E – 1 RT
+ xk 2 e
E – 2 RT
,
(11)
where Eeff is the effective activation energy for the overall process. Assuming, for the sake of simplicity, that k ≈ k1 ≈ k2, the formula for evaluation of Eeff was obtained [20]: E –E
E eff
1 2 ⎛ ⎞ RT = E 1 – RT ln 1 + x ⎜ e – 1⎟ . ⎝ ⎠
(12)
The effective energy of activation decreases with increasing x. Therefore, we can assume here that the unusually low or even negative values of the apparent activation energy appear due to the twostage reac tion, where the first stage is the lowactivated transfor mation of nanocrystalline or amorphous precursors into the crystalline phase. CONCLUSIONS It has been demonstrated that HSTC technique is a powerful tool for investigating the kinetics of heteroge neous gasless reactions in conditions similar to those existing in a combustion wave, which cannot be achieved by conventional DTA/TGA method. It has also been confirmed that highenergy ball milling leads to a significant decrease in reaction onset tem perature as well as in apparent activation energy.
1. Seebauer, V., Petek, J., and Staudinger, G., Effects of particle size, heating rate and pressure on measurement of pyrolysis kinetics by thermogravimetric analysis, Fuel, 1997, vol. 76, no. 13, pp. 1277–1282. 2. Kharatyan, S.L. and Chatilyan, H.A., Nonisothermal kinetics and mechanism of tungsten siliconizing in gas less combustion wave, Int. J. Self.Prop. HighTemp. Synth., 1999, vol. 8, no. 1, pp. 31–42. 3. Thiers, L., Leitenberger, B., Mukasyan, A.S., and Varma, A., Influence of preheating rate on kinetics of hightemperature gas–solid reactions, AIChE J., 2000, vol. 46, no. 12, pp. 2518–2524. 4. Pinheiro, G.F.M., Lourenco, V.L., and Iha, K., Influ ence of heating rate on thermal decomposition of HMX, J. Therm. Anal. Calorim., 2002, vol. 67, no. 2, pp. 445–452. 5. Kharatyan, S.L., Chatilyan, H.A., Mukasyan, A.S., Simonetti, D.A., and Varma, A., Influence of heating rate on kinetics of rapid hightemperature reactions in condensed heterogeneous media: Mo–Si system, AIChE J., 2005, vol. 51, no. 1, pp. 261–270. 6. Grigor’ev, Y.M., Gal’chenko, Y.A., and Merzhanov, A.G., Investigation of the rate of the high temperature reaction between aluminum and oxygen using the ignition method, Combust. Explos. Shock Waves, 1973, vol. 9, no. 2, pp. 162–167. 7. Kharatyan, S.L., Grigor’ev, Y.M., and Merzhanov, A.G., Kinetics of heat release during hightemperature nitra tion of titanium, Izv. Akad. Nauk SSSR, Ser. Met., 1977, vol. 10, no. 2, pp. 178–181. 8. Shteinberg, A.S. and Knyazik, V.A., Macrokinetics of hightemperature heterogeneous reactions: SHS aspects, Pure Appl. Chem., 1992, vol. 64, no. 7, pp. 965– 976. 9. Shteinberg, A.S., Lin, Y.C., Son, S.F., and Mukasyan, A.S., Kinetics of high temperature reaction in Ni–Al Sys tem: Influence of mechanical activation, J. Phys. Chem., Ser. A, 2010, vol. 114, no. 20, pp. 6111–6117. 10. Hobosyan, M.A., Kirakosyan, Kh.G., Kharatyan, S.L., and Martirosyan, K.S., Study of dynamic features of highly energetic reactions by DSC and highspeed tem perature scanner (HSTS), MRS Proc., 2013, p. 1521, MRSF121521000105; DOI:10.1557/opl.2013.144. 11. Hobosyan, M.A., Kirakosyan, Kh.G., Kharatyan, S.L., and Martirosyan, K.S., Reaction dynamics of PTFE/Al2O3 system at various heating rates, Abstr. XII Int. Symp. on SHS, 2013, South Padre Island, TX (USA), pp. 219–220. 12. Nepapushev, A.A., Moskovskikh, D.O., Kirakosyan, Kh.G., Kharatyan, S.L., Rogachev, A.S.,
INTERNATIONAL JOURNAL OF SELFPROPAGATING HIGHTEMPERATURE SYNTHESIS
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28
13.
14.
15.
16.
NEPAPUSHEV et al. and Mukasyan, A.S., Study of high temperature kinet ics in mechanochemically activated Ni–Al system at high heating rates, Abstr. XII Int. Symp. on SHS, 2013, South Padre Island, TX (USA), pp. 57–58. Kirakosyan, Kh.G., Kharatyan, S.L., Nepapushev, A.A., Moskovskikh, D.O., Rogachev, A.S., and Mukasyan, A.S., Some specific features at rapid heating of mecha nochemically activated Ni–Al system, Abstr. XIII Int. Ceramics Congress CIMTEC 2014, 2014, Montecatini Terme (Italy), CB9.5:L03. Kissinger, H.E., Reaction kinetics in differential ther mal analysis, Anal. Chem., 1957, vol. 29, no. 11, pp. 1702–1706. Gasparyan, A.G. and Shteinberg, A.S., Macrokinetics of reaction and thermal explosion in Ni–Al powder mixtures, Combust. Explos. Shock Waves, 1998, vol. 24, no. 3, pp. 324–330. White, J.D.E., Reeves, R.V., Son, S.F., and Mukasyan, A.S., Thermal explosion in Al–Ni system:
17.
18. 19.
20.
Influence of mechanical activation, J. Phys. Chem., Ser. A, 2009, vol. 113, no. 48, pp. 13541–13547. Baghdasaryan, A.M., Hobosyan, M.A., Khachatryan, H.L., Niazyan, O.M., Kharatyan, S.L., Sloyan, L.H., and Grigoryan, Y.G., The role of chemi cal activation on the combustion and phase formation laws in the Ni–Al–promoter system, Chem. Eng. J., 2012, vol. 188, pp. 210–215. Itin, V.I. and Naiborodenko, Yu.S., HighTemperature Synthesis of Intermetallic Compounds, Tomsk: Izd. Tomsk. Univ., 1989, pp. 85–87 (in Russia). Starink, M.J., The determination of activation energy from linear heating rate experiments: A comparison of the accuracy of isoconversion methods, Thermochim. Acta, 2003, vol. 404, nos. 1–2, pp. 163–176. Rogachev, A.S., Shkodich, N.F., Vadchenko, S.G., Baras, F., Kovalev, D.Yu., Rouvimov, S., Nepapushev, A.A., and Mukasyan, A.S., Influence of high energy ball mill ing on structure and reactivity of the Ni + Al powder mixture, J. Alloys Comp., 2013, vol. 577, pp. 600–605.
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