Thermochemical behavior of nano-sized aluminum-coated nickel particles

Transcription

1 J Nanopart Re (2014) 16:2392 DOI / RESEARCH PAPER Thermochemical behavior of nano-ized aluminum-coated nickel particle Dilip Sriniva Sundaram Puneeh Puri Vigor Yang Received: 17 September 2013 / Accepted: 28 March 2014 / Publihed online: 11 April 2014 Ó Springer Science+Buine Media Dordrecht 2014 Abtract Molecular dynamic imulation are performed to invetigate the thermochemical behavior of aluminum-coated nickel particle in the ize range of 4 13 nm, beyond which aymptotic behavior i oberved. The atomic interaction are captured uing an embedded atom model. Emphai i placed on the particle melting behavior, diffuion characteritic, and inter-metallic reaction. Reult are compared with the correponding propertie of nickel-coated nano-aluminum particle. Melting of the hell, which i a heterogeneou proce beginning at the outer urface of the particle, i followed by diffuion of aluminum and nickel atom and inter-metallic reaction. The enuing chemical energy heat up the particle under adiabatic condition. The alloying reaction progreively tranform the core hell tructured particle into a homogeneou alloy. The melting temperature of the hell i weakly dependent on the core ize, but increae ignificantly with increaing hell thickne, from 750 K at 1 nm to 1,000 K at 3 nm. The core melt at a temperature comparable to the melting point of a nacent particle, contrary to the phenomenon of D. S. Sundaram V. Yang (&) School of Aeropace Engineering, Georgia Intitute of Technology, Atlanta, GA 30332, USA vigor.yang@aeropace.gatech.edu P. Puri Department of Mechanical and Nuclear Engineering, The Pennylvania State Univerity, Univerity Park, State College, PA, USA uperheating oberved for nickel-coated aluminum particle. The melting temperature of the core decreae from 1,730 to 1,500 K, when it diameter decreae from 10 to 7 nm. For maller core, the majority of nickel atom participate in reaction before melting. The diffuion coefficient of nickel atom in aluminum hell exhibit a temperature dependence of the form D = D 0 exp(-e A /RT), with an activation energy of kj/ mol and a pre-exponential factor of m 2 /. The adiabatic reaction temperature, alo a ize-dependent quantity, increae with increaing core diameter, attain a maximum value of 2,050 K at 5 nm, and decreae with further increae in the core diameter. The calculated value agree reaonably with thoe obtained via chemical equilibrium analyi. The burning time exhibit trong dependence of particle core ize and hell thickne of the form b = a n d m, where the exponent n and m are 1.70 and 1.38, repectively. The finding further corroborate the fact that the reaction rate i controlled by diffuion proce. Keyword Nano-nickel particle Nanoaluminum particle Inter-metallic diffuion and reaction Metal particle thermodynamic Lit of ymbol A Area Al Aluminum C p Specific heat D Diffuion coefficient d Diameter

2 2392 Page 2 of 16 J Nanopart Re (2014) 16:2392 E A F H k B M m N n Ni P q Q R r T t U V Activation energy Force Enthalpy Boltzmann contant Ma Thickne exponent, ma Number of atom Diameter exponent Nickel Preure Generalizeoordinate Inertia factor Ga contant Poition vector, radiu Thermotat degree of freedom Temperature Thickne Potential energy Volume, pair potential function Greek q Electron denity function d Shell thickne d t Thermal diplacement Burning time b Subcript ad Adiabatic c Core cm Center of ma f Formation i Initial, interface, atom index variable j Atom index variable m Melting p Particle prod Product reac Reactant Introduction Energetic material compoed of nickel and aluminum have been employed in variou propulion and pyrotechnic application (Andrzejak et al. 2007; Reeve et al. 2010; Ficher and Grubelich 1996). They are employed a localized heat ource for chemical and bio neutralization, ultrafat fue, and mart thermal Table 1 Heat of reaction and adiabatic reaction temperature of aluminum-baed inter-metallic reaction (Mori 2001; Mechel and Kleppa 2001; Ficher and Grubelich 1998) Reaction Heat of reaction (kj/mol) 3Ni? Al? Ni 3 Al ,586 Ni? Al? NiAl ,911 2Ni? 3Al? Ni 2 Al ,406 Ni? 3Al? NiAl ,127 Pt? Al? PtAl ,073 Pd? Al? PdAl ,653 Ti? 3Al? TiAl ,591 Fe? Al? FeAl ,423 Reaction temperature, K(T initial = 298 K) barrier (Zhao et al. 2006). Nickel aluminum (Ni Al) ytem i ideal for ituation in which liberation of ga-phae product i not deired, ince the reaction yield only condened-phae product. Table 1 how the heat of reaction and adiabatic reaction temperature for ome of the mot energetic aluminum-baed intermetallic reaction (Mori 2001; Mechel and Kleppa 2001; Ficher and Grubelich 1998). The adiabatic reaction temperature of Ni Al reaction i a high a 1,911 K, greater than thoe of other reaction, with the exception of Pd Al and Pt Al counterpart. Thee demontrate the high energy content of the Ni Al ytem. Conolidated blend of aluminum and nickel powder are widely ued in the combution ynthei of nickel aluminide (Ni x Al 1-x ), which are attractive tructural material for a variety of engineering ytem (Mori 2001). The reactant powder are ignited at one end and a elf-utaining combution wave propagate through the packed mixture. The profound interet in the combution ynthei lie in the implicity anot effectivene of the proce (Aruna and Mukayan 2008). The combution product have relatively low impurity content, ince the flame vaporize volatile contaminant (Li 2003). The efficiency of the proce can be further enhanced by employing nano-ized particle (Hunt et al. 2004), which have unuually favorable phyicochemical propertie due to the preence of a large number of atom on the particle urface. The melting temperature of a 2-nm aluminum particle i 473 K, which i lower than the bulk value of 933 K by 460 K (Puri and Yang

3 J Nanopart Re (2014) 16:2392 Page 3 of ). The ignition temperature and burning time of nano-aluminum particle are alo lower than thoe of their micron-izeounterpart (Huang et al. 2009). Micro-tructural image of the powder blend indicate that the nickel particle are embedded in a continuou aluminum matrix or vice vera (Farber et al. 1998). The geometry of uch a ytem can, thu, be implified a a core hell particle tructure, where the hell repreent the urrounding matrix (Farber et al. 1998). Furthermore, Ni/Al clad particle can be directly employed to ynthei nickel aluminide (Thier et al. 2002). Undertanding their phyicochemical characteritic i, thu, of paramount importance to material ynthei application. A common approach to yntheize Ni/Al core hell tructured particle i the olution proce (Foley et al. 2005). Nacent metal particle are lurried with dimethyl ether (DME) olvent. In a eparate flak, a chemical complex of the coating metal i diolved in DME. The reulting olution i added to the tirred metal lurry and allowed to react at room temperature for 12 h. Thi proce reult in the formation of uniform coating on the parent metal particle. Another ynthei technique i the cyclic electroplating proce (Yih 2000). The particle are immered in a metal ion containing electrolyte, tirred, and allowed to ediment looely on the cathode plate. An electric potential i applied acro the anode anathode plate to depoit metallic ion in the electrolyte on the particle urface. Molecular dynamic (MD) imulation of planar Ni Al ytem have been recently performed (Bara and Politano 2011; Politano et al. 2013). In our previou work (Sundaram et al. 2013), the effect of core ize and hell thickne on the thermochemical behavior of pherical nickel-coated nano-aluminum particle were invetigated. For aluminum-coated nickel particle, uch tudie are yet to be performed. Previou work (Henz et al. 2009; Levchenko et al. 2010) conidered particle with equal number of aluminum and nickel atom. From a purely cientific perpective, a comparative analyi of the phyicochemical propertie of thee two different ytem i intereting and ueful. The preent invetigation will addre thee iue by mean of MD imulation. Emphai i placed on the particle melting behavior, diffuion procee, and inter-metallic reaction. The core diameter cover a range of 2 10 nm, and four different hell thicknee of 0.5, 1.0, 2.0, and 3.0 nm are choen. Theoretical framework The bai of the preent work i the general analyi outlined in our previou work (Sundaram et al. 2013). The atomic interaction are reproduced uing an embedded atom potential function with the parameter developed by Papanicolaou et al. (2003). The potential energy (U) can be expreed a =2 U ¼ XN i¼1 >< X >: j p ab A ab e r ij r 0 1 ab 6 4 X j n 2 ab e 2q ab r ij r 0 1 ab 7 5 >= ; >; ð1þ where r ij repreent the ditance between atom i and j and N i the number of atom. Table 2 lit the parameter of the model. They were obtained by fitting the potential function to the propertie of aluminum, nickel, and nickel-aluminum ordered alloy. For particle conidered in the preent work, phae-equilibrium analyi ugget that the reaction product are B2-NiAl and Al-rich pecie (e.g., NiAl 3 ). It i reauring to note that the potential function reproduce the propertie of thee material with reaonable accuracy. Iobaric iothermal (NPT) enemble i ued to tudy melting and diffuion procee in the preence of external heating at contant preure condition. The equation of motionaregivenby(anderen1980;noe1984) " # M V ¼ P þ 2 3V m i q i ¼ V 1=3 F i 2 Q ¼ V 2=3 X i V2=3 X i 2m i V _ q_ i 3V m i q_ 2 i gk BT m i q_ 2 i V X 1=3 i 2mi _ q _ i F i q i ð2þ where q i i the generalizeoordinate, _q i and q i denote the firt-order and econd-order derivative of q i with Table 2 Parameter of the embedded atom potential function (Papanicolaou et al. 2003) Ni Ni Al Al Ni Al A (ev) n (ev) p q r 0 (Å)

4 2392 Page 4 of 16 J Nanopart Re (2014) 16:2392 repect to time, F i i the net force on atom i, M i the fictitiou ma for volume motion, m i the ma of the atom, V i the volume, P i the preure, T i the temperature, Q i the thermal inertia factor, g i a parameter, k B i the Boltzmann contant, and i the additional degree of freedom. Iochoric ioenergetic (NVE) enemble i employed to invetigate elfheating of the particle due to inter-metallic reaction under adiabatic condition. For the NVE enemble, the equation of motion can be written a m i q i ¼ ou ð3þ oq i The equation of motion are numerically integrated uing a fifth-order predictor corrector algorithm. The time tep i choen a 1 f in order to capture the vibrational motion of the atom accurately. Negligible improvement in the model reult i obtained when the time tep i reduced from 1 to 0.1 f. The heating rate i choen a 10-2 K/f baed on the reult of a parametric tudy conducted in our previou work (Sundaram et al. 2013). Heating rate lower than 10-2 K/f increae the total computational time dramatically with only little change in the model reult. Reult and dicuion Melting of nacent aluminum and nickel particle The theoretical framework i firt employed to analyze melting of nacent aluminum and nickel particle. Figure 1a how the variation of potential energy with temperature for a 9-nm aluminum particle coniting of 23,328 atom. A gradual deviation from the initial linear trend at about 900 K mark the onet of urface melting of the particle. The potential energy difference can be calculated a follow: DEðnÞ ¼ Enþ ð mþ En ð Þ; ð4þ where E i the potential energy and n i the integration tep number. The contant, m, i choen o a to determine the melting point within an accuracy of ±25 K. The reult i hown in Fig. 1b. The urface melting begin at 900 K, a evidenced by an abrupt increae in the potential energy difference. The peak melting rate occur at 1,075 K and phae tranition i complete at 1,200 K. It i important to recognize that nano-particle melt over a range of temperature, a oppoed to iothermal tructural melting of urfacefree bulk material. Note that the melting temperature range increae with increaing heating rate (Sundaram et al. 2013). Figure 2 how the effect of particle ize on the melting temperature of aluminum and nickel particle. The model prediction are compared with the reult of previou MD imulation (Puri and Yang 2007; Sundaram et al. 2013; Qi et al. 2001) and experiment (Eckert et al. 1993; Lai et al. 1998). The ize dependence of melting temperature of nanoparticle i well decribed by the Gibb-Thompon theory T m ðþ¼t r b m 2Tbr! m l H bq ; ð5þ f r where T m i the melting temperature, H f i the latent heat of fuion, q i the olid phae denity, and r i the particle radiu. The ubcript b refer to the bulk material. The reulting value are alo hown in the figure. Note that more ophiticated model that couple phae-field theory to material mechanic have been developed recently (Levita and Samani 2011). The predicted melting temperature are greater than thoe obtained uing the Cleri Roato potential function (Sundaram et al. 2013), but agree reaonably well with the counterpart of the glue potential (Puri and Yang 2007). In the experiment, particle melting wa tudied uing differential canning calorimetry (DSC) (Eckert et al. 1993) and thin-film DSC (Lai et al. 1998) etup, with heating rate on the order of 1 and 10 5 K/, repectively. Thee are order of magnitude lower than the heating rate employed in the preent MD imulation. The melting point increae with increaing heating rate (Lu and Ahren 2003). Furthermore, the experiment conidered paivated particle, while the preent tudy deal with nacent particle. It i well known that that paivated particle exhibit the phenomenon of uperheating (Mei and Lu 2007). For homogeneou melting, the degree of uperheating increae with decreaing particle ize (Mei and Lu 2007). It i, thu, not urpriing that the predicted melting point are greater than the experimental data, epecially for large particle ize. Note that the meaured value of Eckert et al. (1993) and Lai et al. (1998) are different. Thi may be attributed to the difference in the heating rate and fabrication method. Lai et al. particle were prepared uing vaporphae condenation method, wherea Eckert et al.

5 J Nanopart Re (2014) 16:2392 Page 5 of (a) Potential Energy, ev/atom Aluminum end of particle melting tart of urface melting Melting Sundaram et al. Puri and Yang Eckert et al. Lai et al. prediction Gibb- Thompon bulk value Aluminum Particle Diameter, nm (b) Δ E, ev/atom Onet of melting Peak melting rate End of melting Melting Sundaram et al. Qi et al. prediction Gibb-Thompon bulk value Nickel Fig. 1 a Variation of potential energy with temperature for a 9-nm aluminum particle coniting of 23,328 atom, b potential energy difference a a function of temperature howing the onet anompletion of particle melting employed mechanical attrition technique. Figure 2b how the melting temperature of nickel particle calculated by Qi et al. (2001) uing the quantum Sutton Chen force field. They are ignificantly lower than the value obtained in the preent work. A can be een, the embedded atom model with the parameter developed by Papanicolaou et al. (2003) offer accurate prediction of the melting temperature of aluminum and nickel particle. Thermochemical behavior of aluminum-coated nickel particle The thermochemical behavior of aluminum-coated nickel particle i invetigated for different core Particle Diameter, nm diameter and hell thicknee. Emphai i placed on the particle melting behavior, diffuion characteritic, and inter-metallic reaction. The particle i generated by inerting the nickel core into a pherical cavity created in the aluminum particle. Figure 3 how a naphot of the particle cro-ection. The particle i equilibrated at a temperature of 300 K. It i then heated at a contant rate of 0.01 K/f. Figure 4 how the temporal variation of the core radiu and potential energie of the core and hell during equilibration imulation. After an initial tranient phae, the parameter attain their repective equilibrium value. Table 3 how the core diameter ( ), hell thickne (d ), total number of atom (N), and number of nickel atom (N Ni ) of the particle choen in the preent tudy. The core diameter cover the range of 100 Fig. 2 Effect of particle ize on the melting temperature of aluminum and nickel particle

6 2392 Page 6 of 16 J Nanopart Re (2014) 16:2392 δ -3.0 Potential Energy, ev/atom Shell Particle -4.5 Core d p Time, p Fig. 3 Snaphot of a diected aluminum-coated nickel particle (d p =? 2d ) 2 10 nm and four different hell thicknee of 0.5, 1.0, 2.0, and 3.0 nm are conidered. Figure 5 how the key phyicochemical procee during heating of aluminum-coated nickel particle. The time period of concern can be divided into four tage baed on phae tranition and inter-metallic reaction. In the firt tage, the particle i heated to the melting point of the aluminum hell. Solid-tate diffuion i predominant in thi tage. Melting of the aluminum hell, which mark the onet of the econd tage, facilitate the diolution of nickel atom. In the third tage, diffuion of aluminum and nickel atom become more prominent. It tranform the core hell particle into a homogeneou alloy. The enuing exothermic inter-metallic reaction ignificantly heat up the particle. In the following ection, the aforementioned phyicochemical procee are dicued in detail. Melting of hell The bulk melting temperature of aluminum hell i 933 K, which i ignificantly lower than that of nickel core (1,728 K). For aluminum-coated nickel particle, the hell thu melt before the core. In the preent tudy, the melting point i determined baed on the variation of the potential energy with temperature. Thi i hown in Fig. 6. The onet of melting i characterized by a gradual deviation of the potential Core Radiu, nm Time, p Fig. 4 Variation of potential energy anore radiu with time during particle equilibration at a temperature of 300 K energy from the linear trend. For a particle with a core diameter of 3 nm and hell thickne of 2 nm, the melting temperature i predicted to be 930 K. Note that the enuing decreae in the potential energy can be attributed to nickel aluminum reaction. It i important to undertand the mechanim of melting of the hell. Thi can be accomplihed by monitoring the radial variation of a uitable tructural or thermodynamic parameter. Figure 7 how the naphot of the diected particle colored by thermal diplacement of the hell atom. The atomic thermal diplacement i given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 d t;i ¼ r i r 0;i ; ð6þ where r denote the poition vector. The ubcript i and 0 refer to atom i and the initial tate, repectively.

7 J Nanopart Re (2014) 16:2392 Page 7 of Table 3 Configuration of aluminum-coated nickel particle Core diameter ( ), nm Shell thickne (d ), nm Total number of atom (N) Number of nickel atom (N Ni ) , , , , , , ,642 6, ,973 6, ,099 6, ,832 15, ,082 15, ,675 15, ,233 53,754 Potential Energy, ev/atom tart of hell melting =3nm δ =2nm Fig. 6 Potential energy of the hell a a function of temperature for a particle with core diameter of 3 nm and hell thickne of 2nm Stage I (olid-tate diffuion) Stage II (hell melting and diolution of core atom) Stage III (diffuion and inter-metallic reaction) Stage IV (heating of alloyed particle) Fig. 5 Key phyicochemical procee during heating of nanoized aluminum-coated nickel particle The thermal diplacement i a meaure of lattice diorder induced by thermal motion. It i expected to increae abruptly during melting. The naphot indicate that the hell melting i a heterogeneou proce in which the nucleation of the liquid phae begin at the outer urface of the particle. The melting front propagate toward the core hell interface with increaing temperature. Particle core diameter and hell thickne are the two important parameter that affect the melting point of the hell. Figure 8 how the variation of the melting temperature of the hell with the core diameter for a hell thickne of 2 nm. The core ize exert a weak effect on the melting temperature of the hell in the ize range of 2 7 nm. Figure 9 how the effect of hell thickne on the melting temperature of the hell for a core diameter of 7 nm. It increae with increaing hell thickne, from 750 K at 1 nm to 1,000 K at 3 nm. A qualitatively imilar trend wa oberved for other value of core diameter conidered in the preent tudy. A thicker hell typically melt at a higher temperature, ince the percentage of urface atom in the hell decreae with increaing hell thickne. Note that the melting point i weakly dependent on the hell thickne, when the latter exceed 2 nm. In order to undertand the oberved trend, it i imperative to explore the dependencie of the urface-area-to-volume ratio (SVR) of the hell on core diameter and hell thickne.

8 2392 Page 8 of 16 J Nanopart Re (2014) 16: K 1100 δ =2nm Melting K Core Diameter, nm Fig. 8 Effect of core diameter on the melting temperature of the hell for particle with a hell thickne of 2 nm 1040 K 1060 K SVR core ¼ 3 r ; ð7þ SVR hell ¼ 3R2 R 3 r 3 ; ð8þ where r i the core radiu and R i the particle radiu. The reult are hown in Fig. 10. An aymptotic behavior i oberved when the characteritic dimenion attain a critical value. The critical value of core radiu and hell thickne are 4 and 2 nm, repectively. Furthermore, the urface-area-to-volume ratio of the core increae by an order of magnitude, when the core diameter decreae from 10 to 1 nm. For a pherical hell, it increae only by a factor of two. Thee clearly explain the weak dependence of the hell melting point on core ize and aymptotic melting behavior for hell thickne exceeding 2 nm. Deviation of the melting temperature of the hell from it bulk value i negligible for hell thickne greater than 3 nm. Diffuion proce 1.2 t, nm Fig. 7 Snaphot of the particle colored by thermal diplacement of aluminum atom Melting of the hell i followed by outward diffuion of nickel atom. In order to tudy the diffuion of nickel atom, the core radiu i calculated a follow: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u 5 X r c ¼ t NNi 3N Ni i¼1 ðr i r cm Þ 2 ; ð9þ

9 J Nanopart Re (2014) 16:2392 Page 9 of Melting =7nm Shell Thickne, nm Fig. 9 Effect of hell thickne on the melting temperature of hell for particle with a core diameter of 7 nm where r cm i the poition vector of the center of ma. Figure 11a how the variation of the core radiu with temperature for particle with a core diameter of 3 nm and two different hell thicknee of 1 and 2 nm. The core radiu increae harply upon melting of the hell, which implie that the diffuion of nickel atom i a conequence of hell melting phenomenon. Diffuion and enuing inter-metallic reaction are naturally promoted for thinner hell, ince the melting temperature of the hell decreae with decreaing hell thickne. Figure 11b how the trend for particle with core diameter in the range of 3 7 nm and hell thickne of 2 nm. The core ize exert only a weak effect on the diffuion proce, ince the melting temperature of the hell i not a trong function of the core diameter. The inward diffuion of aluminum atom i another phenomenon of interet. To facilitate analyi of thi phenomenon, the particle i divided into eight pherical layer of thickne 0.5 nm, a hown in Fig. 12. Figure 13 how the number of nickel and aluminum atom in each layer a a function of temperature for a particle with a core diameter of 5 nm and hell thickne of 1 nm. Layer 1 5 refer to the nickel core and 6 8 the aluminum hell, repectively. The atom ditribution change negligibly over the temperature range of K. At 1,200 K, nickel atom beneath the interface diffue into the hell, and vice vera for aluminum atom. The diffuion proce i thu bidirectional in aluminum-coated nickel particle. Note that the nickel and aluminum atom are (a) Surface-area-to-volume ratio (SVR), nm -1 (b) Surface-area-to-volume ratio (SVR), nm SVR core =3/r SVR hell =3R 2 /(R 3 -r 3 ) Dimenion (r, δ), nm SVR core =3/r SVR hell =3R 2 /(R 3 -r 3 ) Core Radiu (r), nm Fig. 10 Variation of urface-area-to-volume ratio (SVR) of the core and hell with a core radiu and hell thickne for a core diameter of 7 nm; b core radiu for a hell thickne of 2nm ditributed almot uniformly in the particle, and a homogeneou Ni Al alloy i formed at 2,000 K. The diffuion coefficient of nickel atom in the aluminum hell i an important property, epecially from the tandpoint of development of macro-cale model for ignition anombution. Figure 14 how the effect of temperature on the diffuion coefficient of nickel atom for core diameter in the range of 2 7 nm and three different hell thicknee of 0.5, 1.0, and 2.0 nm. The diffuion coefficient decreae with increaing core diameter, from 1.0 Å 2 /p at 2 nm to 0.33 Å 2 /p at 7 nm for a temperature of 1,600 K. The prediction are comparable to the etimate of Du et al.

10 2392 Page 10 of 16 J Nanopart Re (2014) 16:2392 (a) Core Radiu, nm δ = 2 nm =3nm 1nm δ (b) d p Fig. 12 Schematic of a diected aluminum-coated nickel particle divided into eight pherical layer of thickne d = 0.5 nm Core Radiu, nm =7nm 5nm 3nm (2003), which in turn i benchmarked againt experimental data at macro cale (Ejima et al. 1980; Praizey et al. 2000). The diffuion coefficient exhibit a temperature dependence of the form D ¼ D 0 exp E A RT δ =2nm Fig. 11 Core radiu a a function of temperature for particle with a core diameter of 3 nm and hell thicknee of 1 and 2 nm; b hell thickne of 2 nm anore diameter of 3, 5, and 7nm ; ð10þ where E A i the activation energy and D 0 i the preexponential factor. The curve-fit indicate a value of kj/mol for the activation energy and m 2 / for the pre-exponential factor in the temperature range of 1,000 2,000 K. It i important to note that the diffuion coefficient of aluminum atom are nearly equal to thoe of nickel atom. For example, at a particle ize of 7 nm, the diffuion coefficient of aluminum atom increae from 0.5 to 1.67 Å 2 /p, when the temperature increae from 1,000 to 2,000 K. For temperature lower than 700 K, the diffuion coefficient are in the range of 10-3 to 10-2 Å 2 /p, ignificantly lower than the liquidphae counterpart. Melting of core It wa difficult to clearly acertain the melting temperature of the core, epecially for maller core ize. The alloying reaction, which tranform the nickel core into an alloyed particle, compete with the core melting proce. Figure 15 how the potential energy of the nickel core a a function of temperature for a particle with core diameter of 10 nm and hell thickne of 1 nm. The core begin to melt at a temperature of 1,730 K, which i nearly the bulk melting point of nickel. The melting temperature of the core decreae with decreaing core diameter, from 1,730 K at 10 nm to 1,500 K at 7 nm. For maller core, majority of the nickel atom participate in alloying reaction before melting. Note that the predicteore melting behavior differ from that oberved for nickel-coated aluminum particle. The olid nickel hell exerted a cage-like effect on the aluminum core. A a reult, the melting temperature of the core wa greater than that of a nacent aluminum

11 J Nanopart Re (2014) 16:2392 Page 11 of K -12 =2nm,δ =1.0nm =3nm, δ =1.0nm Number of Ni atom K 1200 K 2000 K 1600 K log e [D (m 2 /)] =5nm, δ =1.0nm =7nm, δ =1.0nm =5nm, δ =0.5nm =2nm, δ =2.0nm Du et al Shell Index K /(RT) Number of Al atom K particle (Sundaram et al. 2013). For aluminum-coated nickel particle, no uch phenomenon i oberved, ince the hell melt before the core. The core melt at a temperature comparable to it counterpart of a nacent nickel particle. Inter-metallic reaction Shell Index 2000 K 800 K 1200 K Fig. 13 Number of nickel and aluminum atom in different pherical hell a a function of temperature for a core diameter of 5 nm and hell thickne of 1 nm The diffuion of nickel and aluminum atom reult in exothermic nickel-aluminum reaction, which ignificantly heat up the particle under adiabatic condition. Figure 16 how the variation of the potential energy a a function of temperature for a particle with a core diameter of 3 nm and hell thickne of 2 nm. The potential energy increae, attain a plateau and then again increae. The trend i characteritic of the core hell particle tructure, and i not oberved for Fig. 14 Diffuion coefficient of nickel atom in aluminum hell a a function of temperature for core diameter in the range of 2 7 nm and three different hell thicknee of 0.5, 1.0, and 2.0 nm (olid line curve-fit D = D 0 exp(-e A /RT), E A = kj/mol, D 0 = m 2 /) Potential Energy, ev/atom =10nm end of melting tart of melting Fig. 15 Potential energy of the core a a function of temperature for a particle with core diameter of 10 nm and hell thickne of 1 nm nacent metal particle. The initial rie in the potential energy i caued by the tranfer of energy from the heat reervoir to the particle. The plateau repreent the tage at which the energy upply i counterbalanced by the chemical energy releae due to intermetallic reaction. The enuing increae in the potential energy ugget the formation of a homogeneou nickel aluminum alloy.

12 2392 Page 12 of 16 J Nanopart Re (2014) 16: Potential Energy, ev/atom Fig. 16 Variation of potential energy with temperature for a particle with core diameter of 3 nm and hell thickne of 2 nm Iochoric ioenergetic MD imulation are performed to tudy inter-metallic reaction, which enable the particle to elf-heat under adiabatic condition. The calculated adiabatic reaction temperature i compared with the value obtained from thermodynamic energy balance analyi. Figure 17 how the Ni Al phae-equilibrium diagram (Maalki 1992). The product of nickel aluminum reaction depend on the particle compoition (Ni:Al atomic ratio) and temperature. In the preent cae, the intermetallic reaction can be expreed a 10:72Al þ Ni! NiAl 3 þ 7:72Al: ð11þ The thermodynamic energy balance i given by H reac ðt i Þ ¼ H prod ðt ad Þ; ð12þ where H reac i the enthalpy of the reactant at an initial temperature, T i, and H prod are the enthalpy of the product at the adiabatic reaction temperature, T ad. The initial temperature i taken a 1,050 K. The enthalpy of the reactant take the form H reac ¼ 10:72H 1;050 K Al þ H 1;050 K Ni þ 10:72H m;al : ð13þ The enthalpy of melting of aluminum i taken a kj/mol. The reulting reactant enthalpy i kj/mol. The total enthalpy of the product i expreed a H prod ¼ 1 t ia Hf;NiAl 298 K V 3 þ C p;nial3 þ 7:72C p:al ð Tad 298Þ þ H m;nial3 þ 7:72H m;al ; ð14þ Liq (Ni) δ α 1000 (Al) ε θ Ni Atomic Fraction Fig. 17 Ni Al phae diagram (e: NiAl 3, d: Ni 2 Al 3, b: NiAl, h: Ni 5 Al 3, and a: Ni 3 Al) (Maalki 1992) where A i the interfacial area, V i the core volume, and t i i the thickne of the interfacial zone. The interfacial core atom participate in reaction prior to melting of the hell, thereby decreaing the particle energy content. The fraction of unreacteore volume depend on the interfacial area-to-volume ratio and thickne of the interfacial reaction zone. The latter i approximated to be 0.7 Å (Henz et al. 2009).The pecific heat, enthalpy of melting, and heat of formation of NiAl 3 are taken a 115 J/mol -K, 38 kj/ mol, and kj/mol, repectively (Mori 2001). The reaction temperature calculated by equating (13) and (14) i 1,420 K. In other word, the particle i elfheated from 1,050 to 1,420 K due to the heat releae from inter-metallic reaction. A more accurate reult can be obtained by conidering the ize dependence of the heat of reaction, pecific heat, and heat of fuion. Figure 18 how the variation of the particle temperature with time under adiabatic condition obtained uing iochoric ioenergetic MD imulation. The initial poition and velocitie of atom are thoe obtained from the iobaric heating imulation at 1,050 K. The particle i heated from 1,050 to 1,540 K over a time period of 100 p. Reaonably good agreement with the reult of thermodynamic analyi i obtained. It i important to note that the atomic pecie are no longer expected to interact with a ground electronic configuration, but with an excited one at higher temperature. Therefore, claical manybody potential reproduce interaction force with only modet accuracy, and ab initio method hould be applied. β

13 J Nanopart Re (2014) 16:2392 Page 13 of (a) Reaction MD imulation Equilibrium analyi (Core-Shell) Equilibrium analyi (Separate) Time, p Fig. 18 Temporal variation of particle temperature under adiabatic condition for a core diameter of 3 nm and hell thickne of 2 nm; iochoric ioenergetic MD imulation It i ueful to undertand the effect of core diameter and hell thickne on the adiabatic reaction temperature of aluminum-coated nickel particle. Figure 19a how the effect of hell thickne on the adiabatic reaction temperature for particle with a core diameter of 3 nm. The reaction temperature decreae from 1,850 to 1,350 K, when the hell thickne increae from 0.5 to 3.0 nm. Thi can be attributed to the change in the compoition of the reaction product. For a hell thickne of 0.5 nm, the alloying reaction take the form 0:55Al þ 0:45Ni! Ni 0:45 Al 0:55 : ð15þ A a reult, all the atom in the particle participate in the alloying reaction to form nickel aluminum alloy. For thicker hell, the reaction can be expreed a xal þ Ni! NiAl 3 þ ðx 3ÞAl: ð16þ The product thu contain unreacted aluminum atom and aluminum-rich nickel aluminum alloy. Satifactory agreement with the reult of thermodynamic analyi i obtained. Figure 19b how the variation of the adiabatic reaction temperature with core diameter for particle with a hell thickne of 1 nm. It increae with increaing core diameter, attain a maximum value of *2,050 K at 5 nm, and decreae with further increae in the core diameter. Chemical equilibrium analyi i performed to calculate the reaction temperature of eparated anore (b) Reaction =3nm Shell Thickne, nm MD imulation Equilibrium analyi (core-hell) Equilibrium analyi (eparate) δ =1nm Core Diameter, nm Fig. 19 Adiabatic reaction temperature of particle a a function of a hell thickne for a core diameter of 3 nm; b core diameter for a hell thickne of 1 nm hell particle. For eparated particle, there i no energy lo due to interfacial pre-mixing proce and the reaction temperature are thu ubtantially greater than thoe obtained via MD imulation. Note that the reaction temperature i maximum when the particle compoition favor the formation of the B2-NiAl, which ha the highet heat of formation on a per molatom bai. Furthermore, the core ize mut be large enough to minimize the lo of energy content due to the interfacial pre-mixing proce. Henz et al. conducted MD imulation analculated the reaction temperature of aluminum-coated nickel particle with equal number of aluminum and nickel atom. The particle ize range of concern wa 3 9 nm. The reaction temperature increaed with increaing core

14 2392 Page 14 of 16 J Nanopart Re (2014) 16:2392 ize, from 1,350 K at 3 nm to 1,525 K at 9 nm. Thi wa attributed to the fact that the energy lo due to the interfacial pre-mixing proce i greater for maller particle. The reaction temperature of Henz et al. are lower than thoe obtained in the preent tudy. One poible reaon i that a different potential function (Finni Sinclair potential) wa employed to capture the interaction between atom. Furthermore, the initial temperature wa taken a 600 K, which i lower than thoe ued in thi tudy (800 1,000 K). Particle burning time i another important property of concern. Figure 20 how the effect of core diameter and hell thickne on the burning time of aluminum-coated nickel particle. The burning time exhibit core ize dependence of the form Burning Time (τ b ), p τ b [p] = 4.97 ( [nm]) 1.70 δ =1.0nm Core Diameter ( ), nm b ¼ ad n c ; ð17þ 300 where i the core diameter in nm, a i the pre-power factor, and n i the diameter exponent. For a hell thickne of 1 nm, n and a are calculated to be 1.70 and 4.97, repectively. The trong dependence of the burning time on particle ize indicate the prevalence of diffuion-controlleondition. The predicted diameter exponent i lower than the value of 2.5 obtained by Henz et al. The effect of hell thickne on the burning time i characterized by the following equation: b ¼ bd m ; ð18þ where d i the hell thickne in nm, b i the pre-power factor, and m i the thickne exponent. For a core diameter of 3 nm, m and b are equal to 1.38 and 42.13, repectively. It i apparent that the core diameter and hell thickne dictate the phyicochemical propertie of aluminum-coated nickel particle. The calculated reaction time i in the range of p, while Henz et al. predicted ignificantly longer burning time (100 1,200 p). Note that both the initial and final temperature in Henz et al. tudy are lower than thoe in the preent work. The diffuion coefficient decreae markedly with decreaing temperature, thereby reulting in longer burning time. It i important to identify key reult of the preent tudy and dicu their general ignificance. For core hell tructured particle with a low melting point hell, the time period of concern can be divided into four tage. In the firt tage, the particle i heated to the melting temperature of the hell. Diffuion of Burning Time (τ b ), p τ b [p] = (δ [nm]) 1.38 =3nm Shell Thickne (δ ), nm Fig. 20 Effect of core diameter and hell thickne on burning time of aluminum-coated nickel particle atom and inter-metallic reaction are not ignificant in thi tage. The olid-phae diffuion coefficient are in the order of 10-3 to 10-2 Å 2 /p, ignificantly lower than the liquid-phae counterpart (0.1 1 Å 2 /p). Melting of the hell, which mark the onet of the econd tage, facilitate the diffuion of core and hell atom. The diffuion proce i accompanied by exothermic inter-metallic reaction which ignite the particle under adiabatic condition. A a reult, the particle ignition temperature i equal to the melting temperature of the hell, a ize-dependent quantity. The melting temperature of the hell i weakly dependent on the core diameter, but decreae ignificantly with decreaing hell thickne. The diffuion

15 J Nanopart Re (2014) 16:2392 Page 15 of proce and inter-metallic reaction are thu promoted for particle with thinner hell. Deviation of the hell melting point from it bulk value i negligible for hell thickne [3 nm. Shell melting i a heterogeneou proce in which the nucleation of the liquid phae begin at the outer urface of the particle. In the third tage, diffuion become more prominent and tranform the core hell particle into a homogeneou alloy. The proce i bidirectional, and the diffuion coefficient of core and hell atom are nearly equal. For particle with a low melting point hell, the phenomenon of uperheating of the core i not oberved. The core melt at temperature comparable to thoe of nacent particle. For maller particle, alloying reaction compete with the melting proce, anore melting i not clearly obervable. The reaction temperature of a core hell particle i a function of the core diameter and hell thickne. It become higher when the particle compoition favor the formation of the product that ha the highet heat of formation on a per mol-atom bai. Furthermore, the core mut be large enough to minimize the lo of energy content due to the interfacial pre-mixing proce. The particle burning time exhibit trong dependence of particle core ize and hell thickne of the form b = a n d m, with the exponent n and m being 1.70 and 1.38, repectively. The finding further corroborate the fact that the reaction rate of a core hell particle i controlled by diffuion proce. Concluion Molecular dynamic imulation were performed to invetigate the thermochemical behavior of aluminum-coated nickel particle in the ize range of 4 13 nm, beyond which aymptotic behavior wa oberved. The atomic interaction were captured uing an embedded atom model. Emphai wa placed on the particle melting behavior, diffuion characteritic, and inter-metallic reaction. Reult were compared with the correponding propertie of nickelcoated nano-aluminum particle. Melting of the hell, which i a heterogeneou proce beginning at the outer urface of the particle, wa followed by diffuion of aluminum and nickel atom and inter-metallic reaction. The enuing chemical energy releae ignificantly heated up the particle. The alloying reaction progreively tranformed the core hell tructured particle into a homogeneou alloy. The melting temperature of the hell wa weakly dependent on the core ize, but increaed ignificantly with increaing hell thickne, from 750 K at 1 nm to 1,000 K at 3 nm. The core melting behavior wa in tark contrat to that oberved for nickel-coated aluminum particle. The nickel core melted at a temperature comparable to the melting point of a nacent nickel particle, ince the hell melted before the core. The melting point of the core decreaed from 1,730 to 1,500 K, when it diameter decreaed from 10 to 7 nm. For maller core, majority of nickel atom diffued and reacted before melting occur. The diffuion coefficient of nickel atom in liquid aluminum hell exhibited a temperature dependence of the form D = D 0 exp (-E A /RT), with an activation energy of kj/mol and pre-exponential factor of m 2 /. The adiabatic reaction temperature increaed with increaing core diameter, attained a maximum value of *2,050 K at 5 nm, and decreaed with further increae in the core diameter. The calculated value agreed reaonably well with thoe obtained via thermodynamic energy balance analyi. The burning time exhibited trong dependence of particle core ize and hell thickne of the form b = ad n c d m, with the exponent n and m being 1.70 and 1.38, repectively. Acknowledgment The author would like to thank the Air Force Office of Scientific Reearch (AFOSR) for their ponorhip of thi program under Contract No. FA The upport and encouragement provided by Dr. Mitat Birkan i greatly appreciated. Reference Anderen HC (1980) Molecular dynamic imulation at contant preure and/or temperature. J Chem Phy 72: Andrzejak TA, Shafirovich E, Varma A (2007) Ignition mechanim of nickel-coated aluminum particle. Combut Flame 150:60 70 Aruna ST, Mukayan AS (2008) Combution ynthei and nanomaterial. Curr Opin Solid State Mater Sci 12:44 50 Bara F, Politano O (2011) Molecular dynamic imulation of nanometric metallic multilayer: reactivity of the Ni-Al ytem. Phy Rev B 84: Du Y, Chang YA, Huang B, Gong W, Jin Z, Xu H, Yuan Z, Liu Y, He Y, Xie FY (2003) Diffuion coefficient of ome olute in FCC and liquid Al: critical evaluation anorrelation. Mater Sci Eng 363: Eckert J, Holzer JC, Ahn CC, Fu Z, Johnon WL (1993) Melting behavior of nanocrytalline aluminum powder. Nanotruct Mater 2:

16 2392 Page 16 of 16 J Nanopart Re (2014) 16:2392 Ejima T, Yamamura T, Uchida N, Matuzaki Y, Nikaido M (1980) Impurity diffuion of fourth period olute (Fe Co, Ni, Cu and Ga) and homovalent olute (In and Tl) into molten aluminium. J Jpn Int Met 44: Farber L, Klinger L, Gotman I (1998) Modeling of reactive ynthei in conolidated blend of fine Ni and Al powder. Mater Sci Eng A 254: Ficher SH, Grubelich MC (1996) A urvey of combution of metal, thermite, and intermetallic for pyrotechnic application. AIAA Paper No Ficher SH, Grubelich MC (1998) Theoretical energy releae of thermite, intermetallic, anombutible metal. In: Proceeding of the international pyrotechnic eminar Foley TJ, Johnon CE, Higa KT (2005) Inhibition of oxide formation on aluminum nanoparticle by tranition metal coating. Chem Mater 17: Henz BJ, Hawa T, Zachariah M (2009) Molecular dynamic imulation of the energetic reaction between Ni and Al nanoparticle. J Appl Phy 105: Huang Y, Riha GA, Yang V, Yetter RA (2009) Effect of particle ize on combution of aluminum particle dut in air. Combut Flame 156:5 13 Hunt EN, Plantier KB, Pantoya ML (2004) Nano-cale reactant in the elf-propagating high-temperature ynthei of nickel aluminide. Acta Mater 52: Lai SL, Carloon JRA, Allen LH (1998) Melting point depreion of Al cluter generated during the early tage of film growth: nanocalorimetry meaurement. Appl Phy Lett 72: Levchenko EV, Evteev AV, Riley DP, Belova IV, Murch GE (2010) Molecular dynamic imulation of the alloying reaction in Al-coated Ni nanoparticle. Comput Mater Sci 47: Levita VI, Samani K (2011) Size and mechanic effect in urface-induced melting of nanoparticle. Nat Commun 2:284 Li HP (2003) An invetigation of the ignition manner effect on combution ynthei. Mater Chem Phy 80: Lu SN, Ahren TJ (2003) Superheating ytematic of crytalline olid. Appl Phy Lett 82: Maalki TB (1992) Binary phae diagram. ASM International, Material Park Mei QS, Lu K (2007) Melting and uperheating of crytalline olid: from bulk to nanocrytal. Prog Mater Sci 52: Mechel SV, Kleppa OJ (2001) Thermochemitry of alloy of tranition metal and lanthanide metal with ome IIIB and IVB element in the periodic table. J Alloy Compd 321: Mori K (2001) Reaction ynthei proceing of Ni Al intermetallic material. Mater Sci Eng A 299:1 15 Noe S (1984) A unified formulation of the contant temperature molecular dynamic method. J Chem Phy 81: Papanicolaou NI, Chamati H, Evangelaki GA, Papacontantopoulo DA (2003) Second-moment interatomic potential for Al, Ni and Ni Al alloy, and molecular dynamic application. Comput Mater Sci 27: Politano O, Bara F, Mukayan AS, Vadchenko SG, Rogachev AS (2013) Microtructure development during NiAl intermetallic ynthei in reactive Ni Al nanolayer: numerical invetigation v TEM obervation. Surf Coat Technol 215: Praizey JP, Garandet JP, Frohberg G, Grieche A, Kraatz KH (2000) Diffuion experiment in liquid metal. In: Proceeding of the firt international ympoium on microgravity reearch & application in phyical cience and biotechnology, pp Puri P, Yang V (2007) Effect of particle ize on melting of aluminum at nano-cale. J Phy Chem C 111: Qi Y, Cagin T, Johnon WL, Goddard WA (2001) Melting and crytallization in Ni nanocluter: the meocale regime. J Chem Phy 115: Reeve RV, Mukayan AS, Son SF (2010) Thermal and impact reaction initiation in Ni/Al heterogeneou reactive ytem. J Phy Chem C 114: Sundaram DS, Puri P, Yang V (2013) Thermochemical behavior of nickel-coated nanoaluminum particle. J Phy Chem C 117: Thier L, Mukayan AS, Varma A (2002) Thermal exploion in Ni Al ytem: influence of reaction medium microtructure. Combut Flame 131: Yih P (2000) U.S. Patent 6,010,610 Zhao S, Germann TC, Strachan A (2006) Atomitic imulation of hock-induced alloying reaction in Ni/Al nanolaminate. J Chem Phy 125:164707

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