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Effect of temperature and O2 pressure on the gaseous species produced during combustion of aluminum
Chemical Physics Letters 649 (2016) 88–91
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Effect of temperature and O2 pressure on the gaseous species produced during combustion of aluminum Vincent Baijot a,b , Jean-Marie Ducéré a,b , Mehdi Djafari Rouhani a,b , Carole Rossi a,b,∗ , Alain Estève a,b a b
CNRS, LAAS, 7 avenue du Colonel Roche, Toulouse F-31400, France Univ de Toulouse, LAAS, Toulouse F-31400, France
a r t i c l e
i n f o
Article history: Received 13 October 2015 In final form 18 February 2016 Available online 24 February 2016
a b s t r a c t Effect of temperature and O2 pressure on the gaseous species produced during the combustion of aluminum is studied using first principles calculations and considering the thermodynamics of the gas phase equilibrium composed of Al, O2 , AlO, Al2 O, AlO2 , Al2 O2 and Al2 O3 . AlO partial pressure dominates all the range of O2 pressures/temperatures. AlO2 is the second most abundant species at low to intermediate temperatures (1200–1727 ◦ C) and Al2 O at higher temperatures (∼3300 ◦ C). Al2 O and Al2 O2 are stable when ionized into mass spectrometer. Al2 O3 , AlO2 and, to a lesser extent AlO, will decompose, hindering their quantitative observation using this technique. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The combustion of aluminum, in the form of particles or layers in contact with an oxidizing environment such as a metal oxide has proved to be useful in a number of applications where high energy densities, gas release or local temperature increase is required [1–3]. Nanoscale arrangements of their basic constituents (Al and oxidizer) has allowed further applications thanks to increased reactivity [4–6], MEMS compatibility [7], and the perspective to tune thermal characteristics [8–10]. This opens the possibility of generating temperature and pressure burst, as well as specific gaseous species, which can be further used in the functional device [1,11]. A very recent attempt to model the delivered pressure impulse, based on the reaction of five different alumino-thermite mixtures (Al/CuO, Al/MoO3 , Al/Bi2 O3 , Al/WO3 , Al/Sb2 O3 ), showed that one major obstacle to the quantitative prediction of combustion pressure is the lack of fundamental understanding of the chemistry taking place during Al reaction [12]. The question addressed in this Letter is to predict the aluminum based gases produced during aluminum combustion and their dependence on Al and O2 partial pressures and on temperature. Most of the knowledge acquired on the production of gas species originates from the seminal mass spectrometry
∗ Corresponding author at: CNRS, LAAS, 7 avenue du Colonel Roche, Toulouse F-31400, France. E-mail address: [email protected] (C. Rossi). http://dx.doi.org/10.1016/j.cplett.2016.02.048 0009-2614/© 2016 Elsevier B.V. All rights reserved.
investigations considering the vaporization of Al–Al2 O3 materials by Inghram et al. [13] (and reference therein). These works demonstrated experimentally that the decomposition of Al-Al2 O3 mixtures heated to 1500 ◦ C–2300 ◦ C under low heating rate, generates multiple gaseous species, namely Al+ , AlO+ , Al2 O+ , Al2 O2 + and O+ with a prevalence of both AlO+ and Al2 O+ species. Since then, a few other experimental and theoretical investigations [14–21] have been performed motivating strong debate on the actual gas phase composition upon aluminum combustion. Timeresolved mass spectrometry experiments (T-jump/TOFMS) [17,18] performed under vacuum (∼10−6 Torr) on Al nanoparticles (nanoAl) and nano-Al mixed with different metal oxides heated to ∼1727 ◦ C under high heating rate (∼105 K/s) clearly indicated the presence of Al+ , Al2 O+ , AlO+ and Al2 O2 + with the prevalence of Al2 O+ species. Other gaseous metal and oxygen from the respective metal oxide is also observed in the mass spectra. Interestingly, another very recent paper by Zachariah and co-workers [22] provided additional data on the role of oxygen partial pressure on nano-Al ignition process, with Al particle of 50 nm in diameter, but did not identify the gaseous species. This last nano-Al ignition study, operated in a wide range of oxygen pressures, from 10−10 atm to 18 atm, naturally questions the uniqueness of the gas phase composition. Is, as may be usually stated from recent mass spectrometry studies, Al2 O always the dominant species? The above preliminary results constitute the motivation of the present study aimed at determining and quantifying, by first principles calculations, the influence of oxygen pressure and temperature on the gas phase equilibrium, considering five molecules: AlO, AlO2 ,
V. Baijot et al. / Chemical Physics Letters 649 (2016) 88–91
Al2 O, Al2 O2 , Al2 O3 . It is worth to be noted here that our model relies on thermodynamic equilibrium which is not always true in fast combustion processes. An out of equilibrium process not only needs a kinetic treatment of the gas phase, using collision cross sections, but is also representative of a particular experiment. On the other hand, an equilibrium process can be generalized to a variety of experimental conditions. We should mention that the equilibrium condition is also extended to possible condensed phase present in the chamber via the coupling of Eqs. (1) and (2). 2. Computational details First, the free energies of all these gaseous species were calculated with Turbomole 6.1 suite of programs [23,24]. Then, the same simulation package was used to screen the various possible molecular decompositions under ionizing conditions. DFT method was used to establish the ground state of the different neutral and ionized molecules. We applied the Contracted Gaussian triple zeta valence plus polarization basis set (def2-TZVP) [25], together with the RI-J approximation [26–28] and the DFT hybrid functional PBE0 [29,30]. The molar free energy Gi0 was determined for each species i through the Turbomole “freeh” modulus as a function of temperature T and for a reference pressure of P0 = 0.1 MPa, except for atomic 0 values were taken from standard NASA-CEA suite of Al where GAl programs databank. All free energies are given in SI-1. We find good agreement of our calculated DFT values of molecular species with “NASA” code databank. The use of DFT calculations for quantifying free energies and other thermodynamics data results from our goal to build an integrated modeling approach for simulating the whole combustion process of an ensemble of energetic particles such as Al and CuO mixtures. The good agreement with results obtained using conventional data shows the relevance of quantum calculations in this type of investigations. The gaseous species considered are O2 , Al, AlO, Al2 O and Al2 O2 , as observed by Inghram et al. [13] with the addition of AlO2 , as observed by Piehler et al. [31] Al2 O3 was also considered on the basis of our previous results [12]. In SI-2, we present polynomial interpolation expressions of the heat capacities, enthalpies and entropies for all species, in standard “NASA” polynomial fits. The perfect gas approximation is considered here as well as in the Turbomole package. The equilibrium composition of the gas phase is obtained using the mass action law, for all possible reactions, with reaction constants involving the Gibbs free energies at the reference pressure P0 . In our case where a large number of molecules of Alxi Oyi type, including Al and O2 , are considered, a generic expression for all gases, at all desired temperatures, can be written as:
0
Pi = P exp
−
Gi0
RT
+ ˛ xi + ˇ yi
(1)
where Pi is the partial pressure of the species i and R is the prefect gas constant. The two parameters ˛ and ˇ are directly determined from the partial pressures of aluminum and oxygen, respectively. Values are given in Supplementary Information file (see SI-3). The oxygen partial pressures are those in Ref. [22], for a direct comparison with experiments. Aluminum partial pressures are taken as the saturated vapor pressure for each reported temperature, i.e. we assume that aluminum in condensed phase is never completely exhausted. The partial pressure PAl (T) is therefore calculated following Eq. (2) [12] where Ui is the vaporization energy, kB is the Boltzmann constant, m is the molecular mass of aluminum, s the area of its surface unit cell (in the condensed phase), and h is the Plank constant.
PAl (T ) =
2mkB3 sh
3
× T 2 × exp
U i
kB T
(2)
89
Concerning the alumina condensed phase, complex chemical mechanisms can take place, involving all types of Alxi Oyi species, and resulting in a non-stoichiometric alumina and an extremely low Al2 O3 saturation vapor pressure. These mechanisms have not been investigated in detail to allow for an accurate calculation of these vapor pressures at all temperatures. The approximate values found in Ref. [12] and used in this Letter are appropriate around the Al2 O3 boiling point at atmospheric pressure. In the following, the observed Al2 O3 vapor pressures are always lower than these approximate saturation values. Within this approximation, we have assumed that no alumina condensed phase exists in the chamber.
3. Results and discussion Figure 1a gives the calculated partial pressures for five basic molecules, namely AlO, AlO2 , Al2 O Al2 O2 and Al2 O3 , as a function of oxygen partial pressure at low combustion temperature: 1200 ◦ C, corresponding to an Al partial pressure of 4.37 Pa. The oxygen pressure varies from 10−5 to 107 Pa, which corresponds to the experimental conditions of Ref. [22]. As expected, partial pressures of each species increase linearly with the O2 pressure. We observe that AlO is by far the most representative molecule in the gas phase at 1200 ◦ C. AlO2 comes next with a slight increase in its slope compared to AlO. AlO2 partial pressure is four orders of magnitude lower than that of AlO under O2 atmospheric pressure. Note that Al2 O partial pressure is roughly 12 orders of magnitude lower than that of AlO all along the oxygen pressure scale. Al2 O2 and Al2 O3 species exhibit even lower partial pressures. This result clearly indicates that at low combustion temperatures, i.e. in the early stages of combustion, the oxidized Al products in the gas phase will be dominated by AlO and AlO2 species to a lesser extent. In order to evaluate potential variations of the gas phase composition as a function of combustion temperature, we also investigated two higher temperatures: 1727 ◦ C which is the exact applied temperature used in T-jump/TOFMS experiments [17], and 3280 ◦ C which is the Al + CuO reaction adiabatic temperature [12]. Figure 1b and c shows the partial pressures of AlO, AlO2 , Al2 O, Al2 O2 and Al2 O3 as a function of the oxygen partial pressures at 1727 ◦ C and 3280 ◦ C, corresponding to Al partial pressures of 4.04 × 103 Pa and 2.14 × 107 Pa, respectively. At 1727 ◦ C, AlO and AlO2 show similar trend as in lower temperature simulation. Interestingly, a shrinking in the relative pressure of Al2 O is observed. 8 orders of magnitude are now separating Al2 O and AlO partial pressures in the all range of calculated O2 pressures. This shrinking makes the Al2 O pressure comparable to the one of AlO2 particularly in the low O2 pressure range (where Al2 O pressure is superior to AlO2 pressure up to 10−3 Pa). Al2 O2 and Al2 O3 species can still be neglected. When the combustion temperature is increased to 3280 ◦ C, two major tendencies are observed. The Al2 O/AlO shrinking is drastically reduced to 4 orders of magnitude (see Figure 1c). As a result, the Al2 O partial pressure is superior to the one of AlO2 in almost all the range of O2 pressures (crossing over at around atmospheric pressure). For what concerns Al2 O2 and Al2 O3 species, their slops are such that they are no more in negligible quantities above the atmospheric O2 pressure (respectively 4–7 orders of magnitude lower than the usually observed Al2 O and less with increasing O2 pressure). From our calculations, there is a transition temperature between 1727 ◦ C and 3280 ◦ C where the Al2 O partial pressure becomes higher than that of AlO2 . However, despite a shrinking AlO/Al2 O ratio with increasing temperature, AlO remains the dominating species which falls in contradiction with mass spectrometry observations [17] giving Al2 O as the dominating species among all other
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V. Baijot et al. / Chemical Physics Letters 649 (2016) 88–91
to be taken with caution due to the limitation of our model to aluminum related mechanisms and also to the lack of information on temperature and quantification of CuO-induced oxygen pressure delivery. For understanding the discrepancy between our findings and mass spectrometry observations, a key point concerns the ionized nature of the detected molecules in mass spectrometry experiments. Here, two mechanisms are to be taken into account. The first is the ionization mechanism by high energy electron impact. The important energy release may lead to a complete fragmentation of the molecule, but the interaction time is very short. This mechanism needs a time dependent DFT modeling of the ionization process. The second mechanism is the spontaneous decomposition of the already ionized molecule during its time of flight, much longer than that of the electron molecule collision. It is this second mechanism that we considered in this Letter and that allows to shed a new light into published data. We should point out that the molecules are no more in interaction with each other inside the mass spectrometer, as a result of the low pressures and the long molecular mean free paths. All thermodynamic and equilibrium considerations being therefore not pertinent, we consider the simple decomposition of the various ionized molecules performing 0 K first principles calculations. The four more representative reactions are reported in the following and all others can be found in the Supplementary Information file (see SI-4) giving a complete overview of our calculations. Al2 O+ → AlO+ + Al, AlO+ → Al+ + O,
E = 398 kJ/mol
E = 70 kJ/mol
Al2 O3 + → Al2 O+ + O2 , AlO2 + → Al+ + O2 ,
Figure 1. Al2 O, AlO2 , AlO, Al2 O2 and Al2 O3 partial pressures as a function of O2 partial pressure at (a) 1200 ◦ C, (b) 1727 ◦ C and (c) 3280 ◦ C corresponding to aluminum vapor pressure of 4.37 Pa, 4.04 × 103 Pa and 2.14 × 107 Pa respectively.
oxidized Al products. In these particular experiments, the Al/CuO nanothermite deposited on an iridium wire is heated up quickly to 1720 ◦ C. Once the combustion is initiated, our findings (AlO to Al2 O shrinking of partial pressures with the temperature) suggest that the temperature is increased concomitantly with the gas production. The T-jump/TOFMS measurements are therefore performed at an actual temperature higher than 1720 ◦ C probably nearer to the Al/CuO adiabatic temperature (3280 ◦ C) where our calculations show that Al2 O is one major component (although not the main) of the gas phase. Moreover, we guess that the combustion pressure is less than the atmospheric pressure since the background pressure in the TOFMS chamber is 4.2 × 10−4 Pa [17]. Note that the direct comparison of our calculations with this latter experiment is
E = −17 kJ/mol
E = −753 kJ/mol
The decomposition energy of Al2 O+ is largely positive and high enough to consider that this decomposition is unlikely to occur in the mass spectrometer confirming that Al2 O is one major molecule produced at high temperatures, as stated in the literature. In turn, AlO+ shows slightly positive decomposition energy. However, if decomposition occurs, the vacuum condition is such that the reverse mechanism will be hindered. We suggest that this slight decomposition can lower its peak intensity in mass spectrometry analysis making Al2 O the dominant species. Ionized Al2 O3 + and AlO2 + show exothermic decomposition energies. This indicates that, even if present in the combustion gas, these molecules will not be observed in the mass spectrometer at their concentration level in the neutral gas phase. As for Al2 O+ the decomposition energy of Al2 O2 + is positive and high enough to consider that the decomposition of this species is unlikely to occur in the mass spectrometer (see SI-3). According to our calculations its presence is conditioned by both a high temperature and a high oxygen pressure. This confirms the experimental observations [13,17], and explains its low concentration probably due to the lack of oxygen pressure in the experiment. 4. Conclusion In conclusion, results plotted in Figure 1 clearly show that the total pressure increases with the increase of combustion temperature and O2 pressure. For an O2 pressure of 100 kPa (1 atm), the total pressure is 1.00 × 105 , 1.05 × 105 , 2.32 × 107 at 1200 ◦ C, 1727 ◦ C and 3280 ◦ C, respectively. Our study concludes that the oxidized aluminum
V. Baijot et al. / Chemical Physics Letters 649 (2016) 88–91
molecules that dominate the combustion of aluminum into oxidizing environment (O2 or metallic oxide) depend on the combustion temperature and oxygen partial pressure. If Al2 O is usually considered as the predominant species in Al + CuO thermites at combustion completion, first principle calculations of the gas phase equilibrium shows that AlO is the main species for all explored experimental conditions, i.e. the pressure and combustion temperatures. Surpassed by AlO2 partial pressure for low to medium temperature regimes, Al2 O, in turn, becomes the second most important contributor to the total pressure at high temperature (3280 ◦ C) and at almost all applied oxygen pressures. Considerations of ionized states of the molecules are also given allowing new insights into spectra analysis. These results are of crucial importance for further quantification of the gas pressure delivered by aluminum-based thermites. Acknowledgments The authors would like to thank the DGA (French Agency for Defense) for its financial support. We also acknowledge the support of CALMIP for computer resources. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2016.02.048. References [1] L. Glavier, G. Taton, J.-M. Ducéré, V. Baijot, S. Pinon, T. Calais, A. Estève, M. Djafari Rouhani, C. Rossi, Combust. Flame 162 (2015) 1813. [2] H. Wang, G. Jian, W. Zhou, J.B. DeLisio, V.T. Lee, M.R. Zachariah, ACS Appl. Mater. Interfaces 7 (2015) 17363. [3] C. Rossi, Al-based Energetic Nano Materials: Design, Manufacturing, Properties and Applications, John Wiley & Sons, Inc, London, UK, 2015.
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[4] M.L. Pantoya, J.J. Granier, Propellants Explos. Pyrotech. 30 (2005) 53. [5] C.E. Aumann, G.L. Skofronick, J.A. Martin, J. Vac. Sci. Technol. B 13 (1995) 1178. [6] Y. Huang, G.A. Risha, V. Yang, R.A. Yetter, Proc. Combust. Inst. 31 (2007) 2001. [7] C. Rossi, K. Zhang, D. Esteve, P. Alphonse, P. Tailhades, C. Vahlas, J. Microelectromech. Syst. 16 (2007) 919. [8] H. Wang, J.B. DeLisio, G. Jian, W. Zhou, M.R. Zachariah, Combust. Flame 162 (2015) 2823. [9] K. Kappagantula, C. Crane, M. Pantoya, Propellants Explos. Pyrotech. 39 (2014) 434. [10] L. Marín, C.E. Nanayakkara, J.-F. Veyan, B. Warot-Fonrose, S. Joulie, A. Estève, C. Tenailleau, Y.J. Chabal, C. Rossi, ACS Appl. Mater. Interfaces 7 (2015) 11713. [11] B.R. Clark, M.L. Pantoya, Phys. Chem. Chem. Phys. PCCP 12 (2010) 12653. [12] V. Baijot, L. Glavier, J.-M. Ducéré, M. Djafari Rouhani, C. Rossi, A. Estève, Propellants Explos. Pyrotech. 40 (2015) 402. [13] J. Drowart, G. DeMaria, R.P. Burns, M.G. Inghram, J. Chem. Phys. 32 (1960) 1366. [14] J. Guo, J. Goodings, A. Hayhurst, Combust. Flame 150 (2007) 127. [15] W. Wang, R. Clark, A. Nakano, R.K. Kalia, P. Vashishta, Appl. Phys. Lett. 96 (2010) 181906. [16] S. Chowdhury, K. Sullivan, N. Piekiel, L. Zhou, M.R. Zachariah, J. Phys. Chem. C 114 (2010) 9191. [17] G. Jian, N.W. Piekiel, M.R. Zachariah, J. Phys. Chem. C 116 (2012) 26881. [18] L. Zhou, N. Piekiel, S. Chowdhury, M.R. Zachariah, J. Phys. Chem. C 114 (2010) 14269. [19] P. Lynch, G. Fiore, H. Krier, N. Glumac, Combust. Sci. Technol. 182 (2010) 842. [20] E.B. Washburn, J.N. Trivedi, L. Catoire, M.W. Beckstead, Combust. Sci. Technol. 180 (2008) 1502. [21] C. Badiola, R.J. Gill, E.L. Dreizin, Combust. Flame 158 (2011) 2064. [22] W. Zhou, J.B. DeLisio, X. Wang, G.C. Egan, M.R. Zachariah, J. Appl. Phys. 118 (2015) 114303. [23] O. Treutler, R. Ahlrichs, J. Chem. Phys. 102 (1995) 346. [24] M.B. Reinhart Ahlrichs, Chem. Phys. Lett. 162 (1989) 165. [25] F. Weigend, R. Ahlrichs, Phys. Chem. Chem. Phys. 7 (2005) 3297. [26] K. Eichkorn, O. Treutler, H. Öhm, M. Häser, R. Ahlrichs, Chem. Phys. Lett. 240 (1995) 283. [27] K. Eichkorn, F. Weigend, O. Treutler, R. Ahlrichs, Theor. Chem. Acc. 97 (1997) 119. [28] F. Weigend, Phys. Chem. Chem. Phys. 4 (2002) 4285. [29] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [30] J.P. Perdew, M. Ernzerhof, K. Burke, J. Chem. Phys. 105 (1996) 9982. [31] T.N. Piehler, F.C. DeLucia, C.A. Munson, B.E. Homan, A.W. Miziolek, K.L. McNesby, Appl. Opt. 44 (2005) 3654.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Effect of temperature and O2 pressure on the gaseous species produced during combustion of aluminum Vincent Baijot a,b , Jean-Marie Ducéré a,b , Mehdi Djafari Rouhani a,b , Carole Rossi a,b,∗ , Alain Estève a,b a b
CNRS, LAAS, 7 avenue du Colonel Roche, Toulouse F-31400, France Univ de Toulouse, LAAS, Toulouse F-31400, France
a r t i c l e
i n f o
Article history: Received 13 October 2015 In final form 18 February 2016 Available online 24 February 2016
a b s t r a c t Effect of temperature and O2 pressure on the gaseous species produced during the combustion of aluminum is studied using first principles calculations and considering the thermodynamics of the gas phase equilibrium composed of Al, O2 , AlO, Al2 O, AlO2 , Al2 O2 and Al2 O3 . AlO partial pressure dominates all the range of O2 pressures/temperatures. AlO2 is the second most abundant species at low to intermediate temperatures (1200–1727 ◦ C) and Al2 O at higher temperatures (∼3300 ◦ C). Al2 O and Al2 O2 are stable when ionized into mass spectrometer. Al2 O3 , AlO2 and, to a lesser extent AlO, will decompose, hindering their quantitative observation using this technique. © 2016 Elsevier B.V. All rights reserved.
1. Introduction The combustion of aluminum, in the form of particles or layers in contact with an oxidizing environment such as a metal oxide has proved to be useful in a number of applications where high energy densities, gas release or local temperature increase is required [1–3]. Nanoscale arrangements of their basic constituents (Al and oxidizer) has allowed further applications thanks to increased reactivity [4–6], MEMS compatibility [7], and the perspective to tune thermal characteristics [8–10]. This opens the possibility of generating temperature and pressure burst, as well as specific gaseous species, which can be further used in the functional device [1,11]. A very recent attempt to model the delivered pressure impulse, based on the reaction of five different alumino-thermite mixtures (Al/CuO, Al/MoO3 , Al/Bi2 O3 , Al/WO3 , Al/Sb2 O3 ), showed that one major obstacle to the quantitative prediction of combustion pressure is the lack of fundamental understanding of the chemistry taking place during Al reaction [12]. The question addressed in this Letter is to predict the aluminum based gases produced during aluminum combustion and their dependence on Al and O2 partial pressures and on temperature. Most of the knowledge acquired on the production of gas species originates from the seminal mass spectrometry
∗ Corresponding author at: CNRS, LAAS, 7 avenue du Colonel Roche, Toulouse F-31400, France. E-mail address: [email protected] (C. Rossi). http://dx.doi.org/10.1016/j.cplett.2016.02.048 0009-2614/© 2016 Elsevier B.V. All rights reserved.
investigations considering the vaporization of Al–Al2 O3 materials by Inghram et al. [13] (and reference therein). These works demonstrated experimentally that the decomposition of Al-Al2 O3 mixtures heated to 1500 ◦ C–2300 ◦ C under low heating rate, generates multiple gaseous species, namely Al+ , AlO+ , Al2 O+ , Al2 O2 + and O+ with a prevalence of both AlO+ and Al2 O+ species. Since then, a few other experimental and theoretical investigations [14–21] have been performed motivating strong debate on the actual gas phase composition upon aluminum combustion. Timeresolved mass spectrometry experiments (T-jump/TOFMS) [17,18] performed under vacuum (∼10−6 Torr) on Al nanoparticles (nanoAl) and nano-Al mixed with different metal oxides heated to ∼1727 ◦ C under high heating rate (∼105 K/s) clearly indicated the presence of Al+ , Al2 O+ , AlO+ and Al2 O2 + with the prevalence of Al2 O+ species. Other gaseous metal and oxygen from the respective metal oxide is also observed in the mass spectra. Interestingly, another very recent paper by Zachariah and co-workers [22] provided additional data on the role of oxygen partial pressure on nano-Al ignition process, with Al particle of 50 nm in diameter, but did not identify the gaseous species. This last nano-Al ignition study, operated in a wide range of oxygen pressures, from 10−10 atm to 18 atm, naturally questions the uniqueness of the gas phase composition. Is, as may be usually stated from recent mass spectrometry studies, Al2 O always the dominant species? The above preliminary results constitute the motivation of the present study aimed at determining and quantifying, by first principles calculations, the influence of oxygen pressure and temperature on the gas phase equilibrium, considering five molecules: AlO, AlO2 ,
V. Baijot et al. / Chemical Physics Letters 649 (2016) 88–91
Al2 O, Al2 O2 , Al2 O3 . It is worth to be noted here that our model relies on thermodynamic equilibrium which is not always true in fast combustion processes. An out of equilibrium process not only needs a kinetic treatment of the gas phase, using collision cross sections, but is also representative of a particular experiment. On the other hand, an equilibrium process can be generalized to a variety of experimental conditions. We should mention that the equilibrium condition is also extended to possible condensed phase present in the chamber via the coupling of Eqs. (1) and (2). 2. Computational details First, the free energies of all these gaseous species were calculated with Turbomole 6.1 suite of programs [23,24]. Then, the same simulation package was used to screen the various possible molecular decompositions under ionizing conditions. DFT method was used to establish the ground state of the different neutral and ionized molecules. We applied the Contracted Gaussian triple zeta valence plus polarization basis set (def2-TZVP) [25], together with the RI-J approximation [26–28] and the DFT hybrid functional PBE0 [29,30]. The molar free energy Gi0 was determined for each species i through the Turbomole “freeh” modulus as a function of temperature T and for a reference pressure of P0 = 0.1 MPa, except for atomic 0 values were taken from standard NASA-CEA suite of Al where GAl programs databank. All free energies are given in SI-1. We find good agreement of our calculated DFT values of molecular species with “NASA” code databank. The use of DFT calculations for quantifying free energies and other thermodynamics data results from our goal to build an integrated modeling approach for simulating the whole combustion process of an ensemble of energetic particles such as Al and CuO mixtures. The good agreement with results obtained using conventional data shows the relevance of quantum calculations in this type of investigations. The gaseous species considered are O2 , Al, AlO, Al2 O and Al2 O2 , as observed by Inghram et al. [13] with the addition of AlO2 , as observed by Piehler et al. [31] Al2 O3 was also considered on the basis of our previous results [12]. In SI-2, we present polynomial interpolation expressions of the heat capacities, enthalpies and entropies for all species, in standard “NASA” polynomial fits. The perfect gas approximation is considered here as well as in the Turbomole package. The equilibrium composition of the gas phase is obtained using the mass action law, for all possible reactions, with reaction constants involving the Gibbs free energies at the reference pressure P0 . In our case where a large number of molecules of Alxi Oyi type, including Al and O2 , are considered, a generic expression for all gases, at all desired temperatures, can be written as:
0
Pi = P exp
−
Gi0
RT
+ ˛ xi + ˇ yi
(1)
where Pi is the partial pressure of the species i and R is the prefect gas constant. The two parameters ˛ and ˇ are directly determined from the partial pressures of aluminum and oxygen, respectively. Values are given in Supplementary Information file (see SI-3). The oxygen partial pressures are those in Ref. [22], for a direct comparison with experiments. Aluminum partial pressures are taken as the saturated vapor pressure for each reported temperature, i.e. we assume that aluminum in condensed phase is never completely exhausted. The partial pressure PAl (T) is therefore calculated following Eq. (2) [12] where Ui is the vaporization energy, kB is the Boltzmann constant, m is the molecular mass of aluminum, s the area of its surface unit cell (in the condensed phase), and h is the Plank constant.
PAl (T ) =
2mkB3 sh
3
× T 2 × exp
U i
kB T
(2)
89
Concerning the alumina condensed phase, complex chemical mechanisms can take place, involving all types of Alxi Oyi species, and resulting in a non-stoichiometric alumina and an extremely low Al2 O3 saturation vapor pressure. These mechanisms have not been investigated in detail to allow for an accurate calculation of these vapor pressures at all temperatures. The approximate values found in Ref. [12] and used in this Letter are appropriate around the Al2 O3 boiling point at atmospheric pressure. In the following, the observed Al2 O3 vapor pressures are always lower than these approximate saturation values. Within this approximation, we have assumed that no alumina condensed phase exists in the chamber.
3. Results and discussion Figure 1a gives the calculated partial pressures for five basic molecules, namely AlO, AlO2 , Al2 O Al2 O2 and Al2 O3 , as a function of oxygen partial pressure at low combustion temperature: 1200 ◦ C, corresponding to an Al partial pressure of 4.37 Pa. The oxygen pressure varies from 10−5 to 107 Pa, which corresponds to the experimental conditions of Ref. [22]. As expected, partial pressures of each species increase linearly with the O2 pressure. We observe that AlO is by far the most representative molecule in the gas phase at 1200 ◦ C. AlO2 comes next with a slight increase in its slope compared to AlO. AlO2 partial pressure is four orders of magnitude lower than that of AlO under O2 atmospheric pressure. Note that Al2 O partial pressure is roughly 12 orders of magnitude lower than that of AlO all along the oxygen pressure scale. Al2 O2 and Al2 O3 species exhibit even lower partial pressures. This result clearly indicates that at low combustion temperatures, i.e. in the early stages of combustion, the oxidized Al products in the gas phase will be dominated by AlO and AlO2 species to a lesser extent. In order to evaluate potential variations of the gas phase composition as a function of combustion temperature, we also investigated two higher temperatures: 1727 ◦ C which is the exact applied temperature used in T-jump/TOFMS experiments [17], and 3280 ◦ C which is the Al + CuO reaction adiabatic temperature [12]. Figure 1b and c shows the partial pressures of AlO, AlO2 , Al2 O, Al2 O2 and Al2 O3 as a function of the oxygen partial pressures at 1727 ◦ C and 3280 ◦ C, corresponding to Al partial pressures of 4.04 × 103 Pa and 2.14 × 107 Pa, respectively. At 1727 ◦ C, AlO and AlO2 show similar trend as in lower temperature simulation. Interestingly, a shrinking in the relative pressure of Al2 O is observed. 8 orders of magnitude are now separating Al2 O and AlO partial pressures in the all range of calculated O2 pressures. This shrinking makes the Al2 O pressure comparable to the one of AlO2 particularly in the low O2 pressure range (where Al2 O pressure is superior to AlO2 pressure up to 10−3 Pa). Al2 O2 and Al2 O3 species can still be neglected. When the combustion temperature is increased to 3280 ◦ C, two major tendencies are observed. The Al2 O/AlO shrinking is drastically reduced to 4 orders of magnitude (see Figure 1c). As a result, the Al2 O partial pressure is superior to the one of AlO2 in almost all the range of O2 pressures (crossing over at around atmospheric pressure). For what concerns Al2 O2 and Al2 O3 species, their slops are such that they are no more in negligible quantities above the atmospheric O2 pressure (respectively 4–7 orders of magnitude lower than the usually observed Al2 O and less with increasing O2 pressure). From our calculations, there is a transition temperature between 1727 ◦ C and 3280 ◦ C where the Al2 O partial pressure becomes higher than that of AlO2 . However, despite a shrinking AlO/Al2 O ratio with increasing temperature, AlO remains the dominating species which falls in contradiction with mass spectrometry observations [17] giving Al2 O as the dominating species among all other
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to be taken with caution due to the limitation of our model to aluminum related mechanisms and also to the lack of information on temperature and quantification of CuO-induced oxygen pressure delivery. For understanding the discrepancy between our findings and mass spectrometry observations, a key point concerns the ionized nature of the detected molecules in mass spectrometry experiments. Here, two mechanisms are to be taken into account. The first is the ionization mechanism by high energy electron impact. The important energy release may lead to a complete fragmentation of the molecule, but the interaction time is very short. This mechanism needs a time dependent DFT modeling of the ionization process. The second mechanism is the spontaneous decomposition of the already ionized molecule during its time of flight, much longer than that of the electron molecule collision. It is this second mechanism that we considered in this Letter and that allows to shed a new light into published data. We should point out that the molecules are no more in interaction with each other inside the mass spectrometer, as a result of the low pressures and the long molecular mean free paths. All thermodynamic and equilibrium considerations being therefore not pertinent, we consider the simple decomposition of the various ionized molecules performing 0 K first principles calculations. The four more representative reactions are reported in the following and all others can be found in the Supplementary Information file (see SI-4) giving a complete overview of our calculations. Al2 O+ → AlO+ + Al, AlO+ → Al+ + O,
E = 398 kJ/mol
E = 70 kJ/mol
Al2 O3 + → Al2 O+ + O2 , AlO2 + → Al+ + O2 ,
Figure 1. Al2 O, AlO2 , AlO, Al2 O2 and Al2 O3 partial pressures as a function of O2 partial pressure at (a) 1200 ◦ C, (b) 1727 ◦ C and (c) 3280 ◦ C corresponding to aluminum vapor pressure of 4.37 Pa, 4.04 × 103 Pa and 2.14 × 107 Pa respectively.
oxidized Al products. In these particular experiments, the Al/CuO nanothermite deposited on an iridium wire is heated up quickly to 1720 ◦ C. Once the combustion is initiated, our findings (AlO to Al2 O shrinking of partial pressures with the temperature) suggest that the temperature is increased concomitantly with the gas production. The T-jump/TOFMS measurements are therefore performed at an actual temperature higher than 1720 ◦ C probably nearer to the Al/CuO adiabatic temperature (3280 ◦ C) where our calculations show that Al2 O is one major component (although not the main) of the gas phase. Moreover, we guess that the combustion pressure is less than the atmospheric pressure since the background pressure in the TOFMS chamber is 4.2 × 10−4 Pa [17]. Note that the direct comparison of our calculations with this latter experiment is
E = −17 kJ/mol
E = −753 kJ/mol
The decomposition energy of Al2 O+ is largely positive and high enough to consider that this decomposition is unlikely to occur in the mass spectrometer confirming that Al2 O is one major molecule produced at high temperatures, as stated in the literature. In turn, AlO+ shows slightly positive decomposition energy. However, if decomposition occurs, the vacuum condition is such that the reverse mechanism will be hindered. We suggest that this slight decomposition can lower its peak intensity in mass spectrometry analysis making Al2 O the dominant species. Ionized Al2 O3 + and AlO2 + show exothermic decomposition energies. This indicates that, even if present in the combustion gas, these molecules will not be observed in the mass spectrometer at their concentration level in the neutral gas phase. As for Al2 O+ the decomposition energy of Al2 O2 + is positive and high enough to consider that the decomposition of this species is unlikely to occur in the mass spectrometer (see SI-3). According to our calculations its presence is conditioned by both a high temperature and a high oxygen pressure. This confirms the experimental observations [13,17], and explains its low concentration probably due to the lack of oxygen pressure in the experiment. 4. Conclusion In conclusion, results plotted in Figure 1 clearly show that the total pressure increases with the increase of combustion temperature and O2 pressure. For an O2 pressure of 100 kPa (1 atm), the total pressure is 1.00 × 105 , 1.05 × 105 , 2.32 × 107 at 1200 ◦ C, 1727 ◦ C and 3280 ◦ C, respectively. Our study concludes that the oxidized aluminum
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molecules that dominate the combustion of aluminum into oxidizing environment (O2 or metallic oxide) depend on the combustion temperature and oxygen partial pressure. If Al2 O is usually considered as the predominant species in Al + CuO thermites at combustion completion, first principle calculations of the gas phase equilibrium shows that AlO is the main species for all explored experimental conditions, i.e. the pressure and combustion temperatures. Surpassed by AlO2 partial pressure for low to medium temperature regimes, Al2 O, in turn, becomes the second most important contributor to the total pressure at high temperature (3280 ◦ C) and at almost all applied oxygen pressures. Considerations of ionized states of the molecules are also given allowing new insights into spectra analysis. These results are of crucial importance for further quantification of the gas pressure delivered by aluminum-based thermites. Acknowledgments The authors would like to thank the DGA (French Agency for Defense) for its financial support. We also acknowledge the support of CALMIP for computer resources. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2016.02.048. References [1] L. Glavier, G. Taton, J.-M. Ducéré, V. Baijot, S. Pinon, T. Calais, A. Estève, M. Djafari Rouhani, C. Rossi, Combust. Flame 162 (2015) 1813. [2] H. Wang, G. Jian, W. Zhou, J.B. DeLisio, V.T. Lee, M.R. Zachariah, ACS Appl. Mater. Interfaces 7 (2015) 17363. [3] C. Rossi, Al-based Energetic Nano Materials: Design, Manufacturing, Properties and Applications, John Wiley & Sons, Inc, London, UK, 2015.
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