Molecular Dynamics Simulation of the Kinetic Reaction of 

Nickel and Aluminum Nanoparticles 

by Brian J. Henz, Takumi Hawa, and Michael Zachariah 

ARL-TR-5134 March 2010 

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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005 

ARL-TR-5134 March 2010 

Molecular Dynamics Simulation of the Kinetic Reaction of 

Nickel and Aluminum Nanoparticles 

Brian J. Henz 

Computational and Information Sciences Directorate, ARL 

and 

Takumi Hawa 

National Institute of Standards and Technology, Gaithersburg, MD 

and 

Michael Zachariah

Department of Mechanical Engineering and the Department of Chemistry and 

Biochemistry, University of Maryland, College Park, MD 

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Molecular Dynamics Simulation of the Kinetic Reaction of Nickel and 

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14. ABSTRACT 

Molecular dynamics simulations are used to simulate the kinetic reaction of nickel (Ni) and aluminum (Al) particles at the 

nanometer scale. The effect of particle size on reaction time and temperature for separate nanoparticles is considered as a 

model system for a powder metallurgy system. Coated nanoparticles in the form of Ni-coated Al nanoparticles and Al-coated 

Ni nanoparticles are also analyzed as a model for nanoparticles embedded within a matrix. The differences in melting 

temperature and phase change behavior, e.g., the volumetric expansion of Al between Al and Ni is expected to produce 

differing results for the coated nanoparticle systems. For instance, the volumetric expansion of Al upon melting is expected to

produce large tensile stresses and possibly rupture in the Ni shell for Ni-coated Al. Simulation results showed that the 

sintering time for separate and coated nanoparticles was nearly linearly dependent upon the number of atoms or volume of the 

sintering nanoparticles. We also found that nanoparticle size and surface energy was an important factor in determining the 

adiabatic reaction temperature for both systems at nanoparticle sizes of less than 10 nm in diameter. 

15. SUBJECT TERMS

Molecular dynamics, self-sustaining high temperature synthesis, nanoparticle

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iii 

Contents 

List of Figures iv

List of Tables v

Acknowledgments vi

1. Introduction 1

2. Simulation Approach 2

3. Thermodynamic Analysis of Separate Nanoparticles 2

4. The Coalescence Processes 5

5. Phenomenological Model of Nanoparticle Reactive Sintering 6

6. MD Simulation Results of Separate Nanoparticle Reactivity 12

7. Reactive Sintering of Core-Shell Nanoparticles 14

7.1 Aluminum-coated Nickel ..............................................................................................14

7.2 Nickel-coated Aluminum ..............................................................................................17

7.3 Analysis of Alloy Formation .........................................................................................19

8. Conclusions 21

9. References 23

List of Symbols, Abbreviations and Acronyms 26

Distribution List 27 
iv 

List of Figures 

Figure 1. Illustration of sintering process showing liquid Al nanoparticle first coating the 

solid Ni nanoparticle and then complete alloying after the Ni nanoparticle has melted. ..........5

Figure 2. Illustration of parameters used in analytical model of reactive coalescence of Ni 

and Al nanoparticles. .................................................................................................................7

Figure 3. (a) Plot of exposed Ni and Al nanoparticle surface area as a function of distance 

between nanoparticle centers and (b) a plot of total exposed surface area as a function of 

distance between nanoparticle centers. These results assume a Ni nanoparticle of radius 

4.53 nm and an Al nanoparticle of 5.23 nm. Notice that the total exposed surface area is 

monotonically decreasing, indicating that the surface energy is also decreasing 

monotonically ............................................................................................................................7

Figure 4. Contact or interface area as a function of center-to-center distance. The contact 

area is increasing as the nanoparticles move closer together (right to left on x-axis). .............9

Figure 5. Total system surface area versus time from mathematical model and MD 

simulations for the sintering of 10-nm-diameter nanoparticles, where the final surface 

area of the NiAl nanoparticle is approximately 480 nm2

. ........................................................10

Figure 6. Cross-sectional view from MD simulations of Ni/Al nanoparticle sintering process 

showing the start of the second stage of coalescence where diffusion is the driving force 

as opposed to contact area maximization. Al atoms are blue and Ni atoms are red. ...............11

Figure 7. Time vs. temperature plot for sintering of separate 10-nm-diameter Al and Ni 

nanoparticles. The various stages if the coalescence processes are denoted on the curve, 

including the final completion stage that occurs after the Ni nanoparticle has melted. .........12

Figure 8. Temperature vs. time in the sintering of nanoparticles with an Ni:Al ratio of 1:1. ......13

Figure 9. Reaction time versus (a) Al nanoparticle diameter, (b) Al nanoparticle surface area, 

and (c) number of Al atoms. Note the nearly linear relationship (dashed line) of reaction 

time between number of atoms (volume) and surface area. ....................................................14

Figure 10. Temperature vs. time in the sintering of Al-coated Ni nanoparticles with an Ni:Al 

ratio of 1:1. ...............................................................................................................................15

Figure 11. Comparison of thermodynamically determined adiabatic temperature for Alcoated Ni nanoparticle and results from MD simulation. .......................................................16

Figure 12. Reaction time versus number of Al atoms in the Al-coated Ni nanoparticle 

system. .....................................................................................................................................17

Figure 13. Comparison of combustion temperature for Ni-coated Al nanoparticle versus Alcoated Ni nanoparticle. ............................................................................................................18

Figure 14. Cross sections of the Ni-coated Al nanoparticle simulation model just after 

melting of the Al core for the (a) 1-nm-thick and (b) 2-nm-thick Ni shells. ...........................19

Figure 15. The results here show the fraction of Ni in each alloy versus fraction of all atoms 

in each alloy, i.e., a data point at (0.25, 0.1) corresponds to 10% of all atoms in the 

system belong to Al3Ni. ..........................................................................................................20
v 

Figure 16. Plot showing spatial distribution of Ni fractions during stages 1 and 2 of the 

sintering process. ......................................................................................................................20

Figure 17. Plot showing spatial distribution of Ni fractions during stage 3 of the sintering 

process......................................................................................................................................21

List of Tables 

Table 1. Change in surface energy versus nanoparticle size. .........................................................4

Table 2. Computed adiabatic temperature versus nanoparticle radius, including contact of 

flat surfaces or infinitely sized spheres. .....................................................................................4
vi 

Acknowledgments 

We would like to acknowledge the support received by the Department of Defense (DoD) 

Supercomputing Resource Center (DSRC) at the Aberdeen Proving Ground, MD. Additional 

support was provided by the National Institute for Standards Technology (NIST) and the U.S. 

Army Research Office (ARO). 
1 

1. Introduction 

Nanoparticles have interesting physical properties that often vary from the bulk material. Some 

of these properties, including increased reactivity (1), are due to the high surface area to volume 

ratio of nanoparticles. With that in mind, nanoparticles may provide enhanced energy release 

rates for explosive and propellant reactions (2). 

There is considerable interest in the self-propagating high-temperature synthesis (SHS) reactions 

of intermetallic compounds because of the associated energy release that takes place (3) during 

the alloying reaction. In addition to the energetic reaction observed in these materials, it is 

possible to produce structural materials that contain this energy release property. Once ignited, 

the SHS reaction releases a large amount of energy in a short period of time. One significant 

difference between SHS and typical combustion processes is that the reactants and products are 

confined to the condensed state (4). The SHS process has many potential applications where heat 

generation is required and oxygen is not available or gaseous products are not desirable. These 

include alloy formation, net-shape processing, propellants, and use as initiators. One of the 

compounds formed from the SHS reaction, and studied here, is nickel aluminide (NiAl). NiAl is 

an important alloy because of its desirable high temperature strength and oxidation resistance (5) 

and the high energy of formation (6). Recently Weihs and coworkers have also used NiAl 

nanolaminate systems in applications of reactive welding (7). 

Not surprisingly since the reaction involves solid starting materials, particle size has a significant 

effect on the properties of the reaction product and the SHS reaction itself (8). The simulation 

and analysis of nanoparticle coalescence without the SHS reaction for like materials is extensive 

(9–14) and involves surface passivation (10), size differences (9, 11), and phase change (9) 

considerations. The analysis here includes all of the previously listed concerns with an additional 

energy release term from the heat of formation. 

The focus of this report is to use atomistic simulation to model the reactive behavior of Ni-Al 

nanoparticles in various configurations. Fortunately, there have been numerous efforts to 

determine accurate empirical potentials for simulating the Ni-Al material system (15). Prior 

simulations using these potentials have investigated the diffusion of Ni and Al atoms (15), pointdefect concentrations in NiAl (16), and plasticity (17), in addition to many other mechanical and 

chemical properties. These efforts have primarily focused on bulk materials rather than 

nanoparticle systems (18), even though there are many manufacturing processes that produce 

nanometer-sized powders for SHS reactions (19). For this simulation effort we have chosen a set 

of embedded atom method (EAM) parameters that reproduce reasonably well the properties of 

Ni, Al, and NiAl in the temperature range of interest. 
2 

2. Simulation Approach 

In this work we employ classical molecular dynamics (MD) with an EAM interatomic potential 

to study the SHS reaction. The EAM is used because of its accuracy and capability to scale up to 

material systems with over 106

 atoms. The MD simulations are compared with thermodynamic 

analyses in order to provide validation of the simulation results and assess the expected energy 

release. 

The MD simulation was conducted using the Large-scale Atomic/Molecular Massively Parallel 

Simulator (LAMMPS) software package (20). For the Ni-Al interactions, the Finnis-Sinclair 

EAM potential (21) from Angelo et al. (22) was used. The Finnis-Sinclair EAM potential allows 

for non-symmetric embedding potential terms, potentially providing improved accuracy for 

metallic alloys (23). In addition to the parameters for NiAl from Angelo et al., other authors have 

developed parameters for the Ni-Al system (16) that may be described by using the FinnisSinclair EAM. 

The three primary nanoparticle sizes that were considered in this work from smallest to largest 

were nanoparticles with 1289, 5635, and 36523 atoms each, which correspond approximately to 

3 , 5, and 10 nm, respectively. The range of sizes was chosen because it represents nanoparticles 

that may be produced in the laboratory and that offer reasonable computational time to conduct 

parametric studies. For the largest system studied, the 10-nm-diameter nanoparticle kinetic 

reaction simulation requires approximately 2 days and 64 processor cores to complete a few 

nanoseconds of simulated time on 3.0 GHz Intel Woodcrest processors. 

3. Thermodynamic Analysis of Separate Nanoparticles 

The separate nanoparticle system is used as a model for powder metallurgy systems where Ni 

and Al particles are compressed into a structural component. In addition to mechanical 

properties, the structural component will contain stored energy for future release through a SHS 

reaction. A thermodynamic analysis of the SHS reaction for the separate Ni and Al nanoparticle 

system is used here to determine the expected trends and data points for simulation validation. In 

the thermodynamic analysis, we are interested in determining the system parameters of the Ni-Al 

nanoparticle system that contribute to the combustion temperature and reaction time. Here we 

have assumed an adiabatic process so that energy released to the surroundings can be ignored. 

This is a good approximation since the reaction occurs on relatively short timescales and the 

nanoparticles are expected to be included in a much larger system where the overall surface to 

volume ratio is small, limiting convective and radiative heat loss. The validity of this assumption 

is explored in a later section. The SHS reaction of an equimolar Ni and Al mixture is written as 
3 

5 0.5 0.5 0.5Ni  0. Al  Ni Al . (1) 

In order to compute the adiabatic temperature for the synthesis reaction, the enthalpy of the 

products and reactants must be equal: 

    H prod Tad  Hreac T0 . (2) 

Assuming that the reaction begins with the reactants at 600 K, above the simulated melting 

temperature of the Al nanoparticles, the enthalpy of the reactants is computed as 

  0.5 0.5 11.85   , ,600 ,600    kJ H H HH reac Al fusion Al K Ni K    mol . (3a) 

This enthalpy result includes the enthalpy of solid Ni and liquid Al (6). The Al nanoparticle is 

assumed to be liquid because for small nanoparticles the melting temperature is known to be 

appreciably below the bulk melting temperature (24). Additionally, for the EAM potential used 

here (22), the aluminum is liquid for these nanoparticle sizes at 600 K. The choice of initial 

temperature will have a nearly linear effect on the adiabatic temperature as long as the 

temperature is between the melting temperature of the Al and Ni nanoparticles. This linear effect 

has been observed in experiments (25) and is a reasonable assumption so long as the heat 

capacities of the solid phases of Ni and NiAl are relatively insensitive to temperature in the 

ranges studied. 

For the products of the SHS process, the enthalpy calculation must take into account 

contributions from the melting of the Ni and the NiAl nanoparticle, enthalpy of formation for the 

NiAl alloy, and changes in surface energy. The first of these, the enthalpies of melting for Ni and 

NiAl, was experimentally determined to be mol

kJ 17.2 and molkJ 31.4 , respectively. The enthalpy 

of mixing for Ni and Al has garnered close scrutiny in the experimental community with a wide 

range of reported values. The enthalpy of formation that is used here was approximately in the 

middle of the reported values at about mol

kJ  65 (6, 26, 27). 

The last contribution to the enthalpy of the products results from the change in surface energy 

due to the reduced total surface area of the combined nanoparticle (28). The contribution to the 

change in system energy from the change in surface area is given as equation 4: 

  Esurf NiAl aNiAl Ni aNi Al aAl          . (4) 

In equation 4, aNiAl , aNi , and aAl are the surface area of the NiAl, Ni, and Al nanoparticles, 

respectively. For the 3-, 5-, and 10-nm Al nanoparticles the reactant surface area is computed 

from the Gibbs surface (29) as 36.32, 98.17, and 343.7 nm2

, respectively. For the associated Ni 

nanoparticles, the surface area is 27.15, 73.59, and 257.87 nm2

, respectively. The surface energy 

is approximately 1115 2 m

mJ for Al and 2573 2 mmJ for Ni at 600 K (30). The surface area of the 

sintered NiAl nanoparticles is 50.77, 137.18, and 480.25 nm2

 for the 3-, 5-, and 10-nm 

nanoparticle cases, respectively. In experimental analysis of the free surface energy of NiAl near 
4 

its melting point, the free surface energy has been reported as 1400 2 m

mJ (31). The approximate 

change in energy versus nanoparticle size is tabulated in table 1. In table 1, the trend is for a 

lower surface energy contribution to the reaction as the nanoparticle size increases. Intuitively, 

one may expect this because the surface area to volume ratio is also decreasing with increasing 

particle size, and therefore has less influence on the sintering process. With the enthalpy of 

formation for NiAl around mol

kJ  65 , the surface energy contribution to the change in enthalpy 

for coalescence of 10-nm-diameter nanoparticles is less than 10% of the total enthalpy change. 

This means that, even at relatively small nanoparticle sizes, e.g., 10 nm, the effect of 

nanoparticle size on energy release is minimal. 

Table 1. Change in surface energy versus nanoparticle size. 

Nanoparticle Radius 

(nm) 

ΔEsurf 

(kJ/mol) 

3 –18.35 

5 –11.41 

10 –6.17 

With the preceding discussion, it is possible to take into account many of the sources of enthalpy 

change in the reaction products including phase and surface area changes. The enthalpy of the 

products is now estimated as 

  melt Ni

T

K

H prod H form NiAl Hsurf Cp NiAl T dT H

ad

,

298

 ,    ,   . (6) 

The heat capacity for solid and liquid NiAl is given in Kubaschewski et al. (21). For the 3-nm 

case, assuming the NiAl nanoparticle melting temperature to be about 1350 K, or the melting 

point of a similarly sized Ni nanoparticle, it is possible to compute the adiabatic reaction 

temperature (table 2). Notice in table 2 that if no surface energy contribution is considered, i.e., 

infinitely large spheres, the final adiabatic temperature is computed to be 1599 K. In section 6, 

we will observe that these results are reasonable and accurately predict the simulated increase in 

temperature attributable to the contribution from the surface energy. 

Table 2. Computed adiabatic temperature versus nanoparticle radius, 

including contact of flat surfaces or infinitely sized spheres. 

Nanoparticle Radius 

(nm) 

Tad 

(K) 

3 2115 

5 1920 

10 1772 

∞ 1599 
5 

4. The Coalescence Processes 

For Ni and Al nanoparticles, the SHS reaction consists of two processes, namely, coalescence 

and alloying. In this work, we have considered the coalescence of a two nanoparticle system with 

an Al and a Ni nanoparticle with an atomic ratio of unity. A complete SHS reaction of this 

system will result in a single NiAl nanoparticle. The MD simulations used to work model 

adiabatic conditions with constant number of atoms and total system energy. The purpose of 

these simulations is to analyze the effect of nanoparticle size on sintering time and adiabatic 

combustion temperature, and to visualize the process. The assumed process is illustrated in 

figure 1. In figure 1, the nanoparticles are initially in contact at a point (a) and the Al 

nanoparticle is larger than the Ni nanoparticle because of the longer Al-Al bond length. The 

simulations are initialized at 600 K so that the Al nanoparticle is liquid and the Ni nanoparticle is 

solid. In figure 1, the sintering process proceeds with the liquid Al nanoparticle initially coating 

the solid Ni nanoparticle while forming some Ni-Al bonds on the surface (b-d). Next, the 

alloying process proceeds with the Ni nanoparticle being heated above its melting point and 

becoming liquid so that mixing may occur (e). The formation of Ni-Al bonds beyond the 

interfacial surface requires diffusion of Al into the Ni nanoparticle or Ni into the liquid Al. Either 

of these processes is possible but since diffusion is a relatively slow process in solid materials it 

is expected that the Ni nanoparticle must melt before the coalescence process proceeds 

appreciably. 

 (a) (b) (c) (d) (e)

Figure 1. Illustration of sintering process showing liquid Al nanoparticle first coating the solid Ni nanoparticle and 

then complete alloying after the Ni nanoparticle has melted. 

The nanoparticle sintering process is driven by two sources of energy as previously discussed. 

The first of these is a decrease in surface area that lowers the total surface energy of the system. 

This energy release mechanism is also observed in the sintering of homogeneous material 

systems such as silicon nanoparticles (28, 32). The second source of energy is from the reactive 

synthesis that occurs initially at the interface between the nanoparticles and later throughout the 

entire system. The energy release from the surface sintering is proportional to the surface area of 

the Ni nanoparticle that is coated by Al and in the whole system to the total number of Ni and Al 

atoms. Additionally, with the temperature increase there is a decrease in the viscosity of the 

liquid Al that will affect the predicted coalescence time. 

Ni Al Ni-Al 
6 

The coalescence of nanoparticles in the liquid and solid phases has been examined extensively 

(9–11). These studies are primarily concerned with the coalescence of two liquid or two solid 

nanoparticles. The analysis for the Ni-Al system requires considering the coalescence of a liquid 

Al nanoparticle and a solid Ni nanoparticle. Lewis et al. (9) considered the coalescence of a 

liquid and a solid gold nanoparticle; this is similar to the situation here except that the material 

system considered was homogeneous. 

In Lewis et al. (9), the author was able to simulate two phases occurring simultaneously for a 

single material by choosing the size of each nanoparticle such that at a specific temperature the 

phase of the nanoparticles was different. Lewis found that coalescence proceeded in two stages: 

first, the contact area was maximized; and second, “sphericization” took place driven by surface 

diffusion. The first stage is much faster than the second and is very similar to the process 

observed here, where the Al nanoparticle maximizes the contact area and partially coats the Ni 

nanoparticle. In this case, there is an added driving force other than the surface energy, 

specifically the energy release on forming of Ni-Al bonds as compared to the Al-Al and Ni-Ni 

bonds. During the second stage, the atoms in the two nanoparticles diffuse and rearrange until 

the system becomes a single spherical nanoparticle. This stage is driven strongly by the 

formation of Ni-Al bonds and is expected to occur on a much shorter timescale than for two 

nanoparticles of the same material. The analytical model and MD simulation results shown in 

sections 5 and 6 explore this assumption. 

5. Phenomenological Model of Nanoparticle Reactive Sintering 

To gain further insight, we have developed a phenomenological model for the reactive sintering 

of Ni and Al nanoparticles. The model includes energy release from surface energy, bond 

formation, and viscous dissipation through deformation. Frenkel (33) has developed a model for 

the coalescence of two homogeneous nanoparticles; however, his model did not account for any 

phase change, kinetic sintering, or heterogeneous materials. Here we extended Frenkel’s model 

to consider the coalescence of two liquid drops to take into account the coalescence of a liquid 

and a solid drop with reactive synthesis. 

The analytical model is initialized with the Al and Ni nanoparticles in contact at a point. The 

distance from nanoparticle center to center is equal to the sum of the respective radii, denoted as 

D in figure 2. The sintering process initially proceeds by the liquid Al nanoparticle coating the 

solid Ni nanoparticle, as illustrated in figure 1. During this phase of the sintering process, two 

sources of energy release are occurring; the first of these is related to the decrease in surface area 

and is proportional to the respective surface tension values. The second source of energy release 

is from the formation of Ni-Al bonds at the interfacial region. Figure 3 is an illustration of the 

parameters used to model the coalescence time. 
7 

rNi

rAl

D

Al

v

vAl

Ni

2a

θ Ni

Figure 2. Illustration of parameters used in 

analytical model of reactive coalescence 

of Ni and Al nanoparticles. 

(a) Center to Center Distance (nm) Exposed Surface Area (nm2

)

0 2 4 6 8 10 0

100

200

300

400

500 Nickel

Aluminum

 (b) Center to Center Distance (nm) Exposed Surface Area (nm2

)

0 2 4 6 8 10 450

500

550

600

650

Figure 3. (a) Plot of exposed Ni and Al nanoparticle surface area as a function of distance between nanoparticle 

centers and (b) a plot of total exposed surface area as a function of distance between nanoparticle centers. 

These results assume a Ni nanoparticle of radius 4.53 nm and an Al nanoparticle of 5.23 nm. Notice that 

the total exposed surface area is monotonically decreasing, indicating that the surface energy is also 

decreasing monotonically 

In figure 2, 2a is the diameter of a circle circumscribed by the contact circumference of the two 

nanoparticles. vAl and vNi are the distance from the Al and Ni nanoparticle surface to the surface 

of the contact circle, respectively. θ is the contact angle as measured from the center of the Ni 

nanoparticle and ranges from 0 to π radians. In order to model the change in energy of the 

coalescing nanoparticle system, three energy change mechanisms must be considered. These 

mechanisms are energy release due to change in surface area, energy release due to kinetic 

reactions at the interface, and energy loss due to viscous dissipation. The rate of energy change 

due to all three must balance at all times. 

The first energy term considered, namely, the surface energy of the nanoparticle system, is 

simply the surface tension times the total exposed surface area. This energy term is written as a 

sum of the Al and Ni nanoparticle contributions: 
8 

,exp ,

s l ES S surf Ni Ni osed Al Al exposed     . (10) 

The exposed area of the Ni nanoparticle can be written as 

2

, 2 42 Ni exposed Ni Ni Ni Ni Ni Ni S S rv r rv      , (11) 

where 

 1 cos  Ni Ni v r . (12) 

Initially, during the sintering process, the Ni nanoparticle is assumed to remain in the solid 

phase, thus maintaining a constant radius. This assumption is reasonable because of the higher 

melting temperature of the Ni nanoparticle. 

The exposed surface area of the Al nanoparticle is written as 

2

, 2 42 Al exposed Al Al Al Al Al Al S S rv r rv      , (13) 

where 

2 2 v r r a Al  Al  Al  (14a) 

  Ni Ni Ni a  v 2r  v . (14b) 

The radius of the Al nanoparticle is computed numerically by using conservation of volume for 

the Al nanoparticle. The exposed surface area of each nanoparticle versus the center to center 

distance is plotted in figure 3a. Notice that although the surface area of the Al nanoparticle 

increases during most of the coalescence process the combined total surface area of the Ni and 

Al nanoparticles decreases monotonically throughout the entire coalescence process. In figure 3, 

the center-to-center distance never reaches zero because the coalescence is considered complete 

once the Ni nanoparticle is completely enveloped by the Al nanoparticle. 

The second source of energy release, namely, the reactive synthesis term, is considered by 

assuming a constant surface density of the Ni nanoparticle and the transient contact area of the 

Ni-Al interface: 

reactive Ni surface erface Vbondenergy E   a   , int . (15) 

The surface density term,  Ni,surface , is proportional to the number of Ni-Al bonds at the contact 

interface. The surface density and bond energy terms, Vbondenergy , can be combined into a single 

constant that defines the energy release per unit area of interface: 

density Ni surface Vbondenergy     , . (16) 
9 

The interfacial contact area is a function of the distance between nanoparticle centers (figure 4). 

The interfacial area increases monotonically until the Ni nanoparticle surface is completely 

covered. This result is expected since the reactive energy term is negative, or releases energy 

during the entire process, in addition to the minimization of surface energy that is driven by the 

surface tension of Ni and Al. The interfacial area is written as 

erface Ni Ni a 2v r int  , (17) 

where Ni v is a function of  as given in equation 12. 

Center to Center Distance (nm)

Contact Area (nm2

)

0 2 4 6 8 10 0

50

100

150

200

250

300

Figure 4. Contact or interface area as a function of center-to-center 

distance. The contact area is increasing as the nanoparticles 

move closer together (right to left on x-axis). 

The third energy term represents the viscous dissipation due to deformation of the Al 

nanoparticle. This viscous dissipation is a function of the viscosity in the liquid Al nanoparticle 

and the rate of deformation. The extent of the viscous flow can be specified by the decrease in 

distance between the center of each drop, and the surface of contact with the Ni nanoparticle. A 

velocity gradient, , can be defined as  dt Al d D /r . The energy dissipated in the whole body per unit 

time is, therefore, approximately 

  2

3

3 ,0

8

0

2 2

,0

2 4 



 



    dt

dD

r dr r

dt

dE Al

r

viscous

Al

     , (18) 

where  is the viscosity of liquid Al and Al,0 r is the initial radius of the Al nanoparticle. 

By conservation of energy, the rate of coalescence can now be computed: 
10 

dt

dE

dt

dE

dt

dEviscous surf reactive   (19a) 

    Al osed Ni Ni

l

Ni osed Al

s

Al Ni v r

dt

d S S

dt

d

dt

dD

r   ,exp  ,exp 2

2

3

3 ,0

8       

 



 (19b) 

After writing equation 19b in terms of d/dt and simplifying the right and left hand sides, we 

find that equation 19b is only linearly dependent on d/dt. Even with this simplification, 

equation 19 is most easily solved numerically using an iterative solver. In order to solve equation 

19b, we need some physical properties of Al, Ni, and NiAl. The dynamic viscosity of bulk 

molten Al at the melting temperature is about   Pa s 3  1.3 10 (34). Based upon a comparison of 

the configurational energy in MD simulations of separate nanoparticles and Al-coated Ni 

nanoparticles, the energy release per unit area,  density , is estimated to be 20.7 2 nm

eV . This number 

is computed by subtracting the system energy of an Al-coated Ni nanoparticle system from the 

energy of a system with separate nanoparticles and dividing by the interfacial surface area. This 

method results in the net change in energy during coating of the Ni surface with Al since some 

Al-Al bonds are lost during the coating process while some Ni-Al bonds are formed at the 

interface. By numerically solving equation 19b, we are able to compute the contact angle, , as a 

function of time and relate this to total exposed surface area of the coalescing nanoparticles. This 

result is presented in figure 5 along with a comparison to the MD simulation results. 

Time (ps)

Surface Area (nm2

)

0 20 40 60 80 480

500

520

540

560

580

600

620

Surf. Area, MD

Surf. Area, Model

Figure 5. Total system surface area versus time from mathematical 

model and MD simulations for the sintering of 10-nm-diameter 

nanoparticles, where the final surface area of the NiAl 

nanoparticle is approximately 480 nm2

. 
11 

Although qualitatively the results in figure 5 show similar trends, the absolute rate of 

coalescence is slightly under predicted by the model. This difference can be attributed to the 

obvious simplicity of the model and more specifically to the difficulty in obtaining accurate 

material parameters. For instance, it is difficult to compare the viscosity of a nanoparticle to the 

bulk material (12), and since the coalescence time is linearly dependent upon the viscosity a 

change in viscosity is directly proportional to a change in modeled coalescence time. 

Additionally, the energy release per unit area term assumes that the net change in energy due to 

the addition of Ni-Al bonds at the interface is a constant value. This is likely not completely 

accurate since fewer Al bonds must be broken to form new Ni-Al bonds during the initial contact 

of the nanoparticles. However, the deviation in this energy release term is likely to be minimal. 

The deviation of the model time from the simulation results at about 50 ps is due to the switch 

from stage 1 to stage 2 in the kinetic coalescence process as described by Lewis et al. (9). As 

described by Lewis, during stage 2, surface diffusion is the predominant factor in continued 

coalescence and is a much slower process than contact area maximization. The actual simulation 

results, as compared with the illustration in figure 1, of the observed coalescence process are 

given in figure 6. 

 Initial Stage 1 Stage 2 Completed 

 Fast (50 ps) Slow (450 ps) Slow (400+ ps) 

Figure 6. Cross-sectional view from MD simulations of Ni/Al nanoparticle sintering process showing the start of 

the second stage of coalescence where diffusion is the driving force as opposed to contact area 

maximization. Al atoms are blue and Ni atoms are red. 

In figure 6, each of the steps in the coalescence process is shown with plots from an MD 

simulation of the coalescence of 10-nm-diameter Al and Ni nanoparticles. The correlation of the 

sintering stages to the reaction temperature and time is illustrated in figure 7 for the sintering of 

separate 10-nm-diameter nanoparticles. In the initial step, the liquid Al nanoparticle (the blue 

atoms in figure 6) has melted and is spherical in shape. The solid Ni nanoparticle (the red atoms) 

has large faceted sides and is a single crystal, a typical configuration for a crystalline 

nanoparticle at low temperatures. During stage 1, the Al nanoparticle is attracted to the Ni 

surface because of the dual driving forces of surface energy minimization and Ni-Al bond 

formation. This period lasts about 50 ps in this simulation as noted in figures 6 and 7. Between 

stages 1 and 2, the driving forces associated with the surface energy are counteracted by a 

resistance to flow in the Al nanoparticle, causing the coalescence process to slow down 

dramatically. During stage 2, lasting about 450 ps, the surface area is not changing so that energy 
12 

release from the surface energy terms has ceased to contribute to the change in system potential 

energy. The subsequent energy release is entirely attributable to the formation of Ni-Al bonds. 

This stage lasts a much longer time than the initial nanoparticle coalescence stage and is 

governed by the material diffusion coefficients. Initially, at stage 2, the Ni nanoparticle is still 

solid and the formation of Ni-Al bonds is only possible by Al diffusing into the Ni core or Ni on 

the surface of the core melting and diffusing away from the interface. This process proceeds until 

the Ni core has reached its melting point and mixing of the remaining Ni and Al atoms occurs 

more rapidly, driven by the enthalpy of formation of NiAl. From stage 2 until complete alloying 

has occurred, taking approximately 400 ps, diffusion and mixing of Ni and Al atoms is the 

primary driving force. 

Time (ps)

Temperature (K)

0 200 400 600 800 1000 400

600

800

1000

1200

1400

1600

1800

Stage 1 (0-50ps)

Stage 2 (50ps-500ps)

Completion (500ps+)

Figure 7. Time vs. temperature plot for sintering of separate 

10-nm-diameter Al and Ni nanoparticles. The various 

stages if the coalescence processes are denoted on the 

curve, including the final completion stage that occurs 

after the Ni nanoparticle has melted. 

6. MD Simulation Results of Separate Nanoparticle Reactivity 

We have previously predicted the adiabatic temperature and sintering time for the reactive 

sintering process of separate equimolar nanoparticles of Al and Ni. In figure 8, the MD 

simulation results for the equimolar nanoparticles are plotted along with the computed adiabatic 

temperature for each considered particle size. 
13 

Time (ps)

Temperature (K)

0 500 1000 1500 400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

Al1289, Ni1289

Al5635, Ni5635

Al36523, Ni36523

Predicted Tad

Figure 8. Temperature vs. time in the sintering of nanoparticles 

with an Ni:Al ratio of 1:1. 

Note: The subscripts in the legend refer to the number of atoms of each 

material and correspond to nanoparticles of diameter 

approximately 3, 5, and 10 nm. The color-coded dashed lines are 

the computed adiabatic temperature from the thermodynamic 

analysis. The black dashed line is the predicted temperature for 

coalescence of bulk Al and Ni. 

From figure 8, it is apparent that the predicted adiabatic temperature is in close agreement with 

the simulated temperature. Variability of the computed temperature arises from the wide range of 

experimental results for the surface tension for liquid Al and solid Ni, the reported enthalpy of 

formation for NiAl, and the assumed melting temperature for the Ni and NiAl materials at this 

scale. Each of these experimental data points is used in the thermodynamic analysis and 

contributes to the small inaccuracies in the predicted temperature. 

The characteristic time for reactive synthesis that we use here is defined by Zhao et al. (35) as t

when 

    0 8 1 0 T t  T  0. T T , (20) 

where T0 is the initial temperature, T1 is the maximum size dependent temperature reached, and 

T t is the transient temperature. The computed reaction times are given in figure 9 and illustrate 

that the time required for separate nanoparticles to react has a power law relationship between 

nanoparticle volume (3) and surface area (2). This implies that not only will the reaction 

temperature be higher, but it will occur more rapidly with decreases in particle size, to a power 

of about 2.5. This is important because a high rate of energy release is desirable for many 

applications. 
14 

(a) Particle Diameter (nm) Reaction Time (ps)

2 3 4 5 6 7 8 9 10 11 0

100

200

300

400

500

600

700

Al Particle Size

(b) Surface Area (nm2

)

Reaction Time (ps)

0 100 200 300 400 0

100

200

300

400

500

600

700

Al Particle SA

(c) No. Al Atoms Reaction Time (ps)

0 10000 20000 30000 40000 0

100

200

300

400

500

600

700

No. Al Atoms

Figure 9. Reaction time versus (a) Al nanoparticle diameter, (b) Al nanoparticle surface area, and (c) number of Al 

atoms. Note the nearly linear relationship (dashed line) of reaction time between number of atoms (volume) 

and surface area. 

By observing the MD simulations and analyzing the shape of the curves in figure 8 for 

temperature versus time, we have surmised that there are two reaction rates to consider. The first 

is during the coalescence process (called the growth rate [see 0 to 500 ps for Al36523 curve in 

figure 8]) and Ni nanoparticle melting, and the second is the rapid formation of the NiAl alloy 

from liquid Al and Ni (convergence rate [see 500 ps and later for the Al36523 curve in figure 8]). 

The temperature at which the transition occurs is size dependent because the melting temperature 

of the Ni nanoparticle is also size dependent. If the process is not perfectly adiabatic, and some 

heat is lost to the surroundings, it is also possible that the first process would not proceed far 

enough for the Ni nanoparticle to melt, and thus the reaction would halt. This would only occur 

with larger nanoparticles that require longer reaction times during which some energy loss to the 

surroundings is likely. This is an important consideration in real-world applications that are not 

perfectly adiabatic, but when complete alloying is desired. One reason for this observed increase 

in reaction rate is because the heat generated from the formation of Ni-Al bonds will conduct 

into the core nanoparticle so that when the reaction front reaches the inner atoms they will have a 

higher diffusion coefficient, which in turn increases the reaction rate. 

7. Reactive Sintering of Core-Shell Nanoparticles 

7.1 Aluminum-coated Nickel 

In this section, we discuss the sintering process for an Al-coated Ni nanoparticle followed by a 

discussion of a Ni-coated Al nanoparticle. Both of these systems can be used as a model for 

highly compacted Ni and Al nanoparticles or one material serving as a matrix for nanoparticles 

of the other. In the first model system, we assume that a Ni nanoparticle has been coated with Al 

and equilibrated without the Ni melting or any further reaction occurring. Results for the reaction 

time and temperature are presented and a comparison with the separate nanoparticle case is 

given. Here again, we have considered three system sizes with 1289, 5635, and 36523 atoms 

each of Al and Ni. 
15 

An initial estimate is that the coalescence process for the fully coated nanoparticle system will be 

a truncated version of the separate nanoparticle case. In the coated nanoparticle system, we do 

not have the first stage of coalescence occurring and only observe the second stage, namely, 

diffusion of Ni and Al atoms to form Ni-Al bonds. The sintering temperature versus time plot is 

given in figure 10 and shows an interesting result. Whereas the maximum temperature reached 

increases with decreasing nanoparticle size for coalescence of separate nanoparticles, the 

opposite is true here: the temperature decreases with decreasing nanoparticle size. 

Time (ps)

Temperature (K)

0 500 1000 1500 2000 500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

Al1289, Ni1289

Al5635, Ni5635

Al36523, Ni36523

Figure 10. Temperature vs. time in the sintering of Al-coated 

Ni nanoparticles with an Ni:Al ratio of 1:1. 

In figure 10, the observed decrease in adiabatic temperature is due to the fact that the ratio of 

atoms near the interfacial region to the atoms in the bulk nanoparticle decreases as the 

nanoparticle size increases. Atoms in the interfacial region have already formed Ni-Al bonds and 

are, therefore, already at a lower configurational energy than if they were contained in a 

homogeneous nanoparticle of either pure Al or Ni. If we extend the adiabatic temperature 

relationship to infinitely large particles, we would approach the result obtained from the analysis 

of separate nanoparticle as they increase in size. The thermodynamic analysis is similar except 

that the surface energy term is zero and the enthalpy of formation is lowered by a factor 

proportional to the ratio of surface area to volume. The enthalpy of the products, equation 6, 

modified for coated nanoparticles becomes 

  melt Ni

T

K

form NiAl p NiAl

surface

prod H C T dT H

V

t A

H

ad

,

298

1 ,  ,  













     , (21) 

where t is a computed thickness value for the interfacial layer, Asurface is the area of the interfacial 

region, and V is the volume of the Ni core. In order to determine the correct empirical thickness 

value,t , for equation 21 we have used the adiabatic temperature computed in the MD simulation 
16 

results for the Al-coated Ni nanoparticle. These results indicate that an interface thickness of 

0.07 nm is able to accurately predict the adiabatic temperature observed in the MD simulations 

(figure 11). In figure 11, it is apparent that the adiabatic combustion temperature is highly size 

dependent for nanoparticles of less than 10 nm in diameter. For very small nanoparticles, less 

than 1 nm diameter, there is little predicted change in temperature from the initial temperature of 

600 K since most of the potential Ni-Al bonds have already been formed. 

Radius (nm)

Combustion Temperature (K)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 400

600

800

1000

1200

1400

1600

1800

Tadiabatic

MD Simulation

Figure 11. Comparison of thermodynamically determined 

adiabatic temperature for Al-coated Ni nanoparticle 

and results from MD simulation. 

From the sintering of separate nanoparticles, it is expected that the reaction time will be linearly 

related to the radius of the nanoparticle to a power of about 2.5. In figure 12, this appears to be 

the case for this range of nanoparticle sizes. A slight deviation from the separate nanoparticle 

result is probably related to the fact that the coalescence process, stage 1, is not included in this 

model system and diffusion takes longer to initialize the kinetic reaction process. 
17 

Radius (nm)

Reaction Time (ps)

1 2 3 4 5 6 0

200

400

600

800

1000

1200

Figure 12. Reaction time versus number of Al atoms in the 

Al-coated Ni nanoparticle system. 

The results for the Al-coated Ni nanoparticle indicate the trends that one might expect from a 

material system that included an Al matrix with embedded Ni nanoparticles. From the results in 

figures 11 and 12, there are two competing reaction results, namely, reaction time and maximum 

temperature. In figure 12, we see that as the Ni nanoparticle size decreases the reaction time 

decreases, causing the energy release rate to increase. A second observation that can be made 

from figure 11 is that the reaction temperature decreases with decreasing Ni nanoparticle size, 

potentially minimizing the effect of the rapid energy release. 

Looking more closely at the reaction time versus number of atoms for the separate nanoparticle 

and Al-coated Ni nanoparticle cases, we observe a similar relationship of reaction time to 

nanoparticle size as that found in separate nanoparticles. In both cases, the reaction time appears 

to have a power law relationship with radius, with an exponent of 2.5. The accelerated 

temperature increase in figure 10 after about 900 ps for the Al36523 curve is the convergence rate 

discussed previously. 

7.2 Nickel-coated Aluminum 

The Ni-coated Al nanoparticle system has garnered some interest because when Al melts there is 

an experimentally observed increase in volume of about 6.5%. This increase in volume creates a 

large stress in the Ni coating and may result in catastrophic failure and fragmentation of the 

nanoparticle (18). In the work by Delogu (18), the fragmentation is only observed for a specific 

set of conditions including Ni shell thickness. In this work, even with the appropriate Ni shell 

thickness, fragmentation of the nanoparticle is not observed. With the empirical potentials and 

parameters considered here, the kinetic alloying reaction is fast and results in a liquid NiAl 

nanoparticle without fragmentation. 
18 

In the first set of analyses, the Ni shell contains the same number of atoms as the Al core. This 

results in an Al core with a radius of 2.8 nm and a Ni shell of about 0.7 nm. Since the bond 

length of Ni is less than Al, the shell is thinner and the contact area is initially greater than 

observed in similarly sized Al-coated Ni nanoparticles. As with the nanoparticle coalescence 

simulations, the temperature of the system is raised to 600 K, at which time a constant energy 

simulation is used to analyze the energy conversion rate and the adiabatic temperature rise of the 

system. 

In the initial simulations with an atomic ratio of unity, there are more Ni-Al bonds in the Nicoated nanoparticle than the Al-coated nanoparticle. It may, therefore, be expected that the total 

system energy would initially be lower in the Ni-coated Al nanoparticle system than the Alcoated Ni system. In fact, the opposite is true, because although there are more Ni-Al bonds in 

the Ni-coated system there are fewer Ni-Ni bonds than in the Al-coated nanoparticle. Since NiNi bonds are stronger than Al-Al bonds, the total initial energy is lower in the Al-coated Ni 

nanoparticle system. Since the final configuration of both systems is a completely alloyed NiAl 

nanoparticle, the system energy change for the Ni-coated nanoparticle is greater than the Alcoated system. This greater change in potential energy results in the computed adiabatic 

temperature for the Ni-coated Al nanoparticle being higher than the Al-coated nanoparticle 

(figure 13), although the difference is not large. 

Time (ps)

Temperature (K)

0 100 200 300 400 500 500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

Al5635, Ni5635, Ni-Coated Al

Al5635, Ni5635, Al-Coated Ni

Figure 13. Comparison of combustion temperature for Ni-coated 

Al nanoparticle versus Al-coated Ni nanoparticle. 

In the two following simulations, we simulated an approximately 5-nm-diameter Al nanoparticle 

coated with either a 1- or 2-nm-thick Ni coating. For these simulations the temperature was 

controlled using an NVT ensemble. This temperature control was used in order to rapidly 

increase the temperature from about 300 K to above the melting point of the Al nanoparticle at a 
19 

rate of 0.1 K/ps. When the Al nanoparticle melts and expands, a large sudden increase of stress 

in the Ni coating is observed. For the 2-nm-thick Ni coating, the increase in stress is not high 

enough to cause failure of the coating. In this case, the outer shell expands slightly but does not 

crack. For the 1-nm-thick case, the stress in the Ni shell is high enough to cause failure. When 

the shell fails, the Al begins to leak out onto the surface of the nanoparticle but no fragmentation 

is observed. If the nanoparticle were surrounded by oxygen, this may initiate the Al oxidation 

reaction, releasing additional energy as Al oxides are formed. 

The cracking and leaking of Al onto the surface of the Ni shell (figure 14) is very different from 

what Delogu (18) observed using a semi-empirical tight-binding (TB) potential. Another 

difference from the work by Delogu is the choice of Al core radius. For both of the shell cases 

here, the core has a radius of 2.8 nm, this is in contrast to the core radius of 3.0 and 2.0 nm for 

the 1.0- and 2.0-nm shell cases, respectively, used by Delogu (18). Since the 1-nm shell case is 

the most interesting and the radii are very close (2.8 vs. 3.0 nm), the choice of core size is not 

expected to have had an appreciable effect on the results for this case. 

(a)

(b)

Figure 14. Cross sections of the Ni-coated Al nanoparticle simulation model just after melting of the Al 

core for the (a) 1-nm-thick and (b) 2-nm-thick Ni shells. 

7.3 Analysis of Alloy Formation 

During the sintering of Ni and Al nanoparticles, numerous local atomic ratios may be identified 

from the Ni-Al binary system (32–34). The data presented here are computed from the 

simulation results by calculating the local atomic ratios. These ratios are computed in order to 

analyze the spatial and temporal distribution of alloys in the simulation. The most commonly 

observed alloys for the Ni-Al binary system include Al9Ni2, Al3Ni, Al3Ni2, NiAl, Ni5Al3, and 

Ni3Al (33) corresponding to Ni fractions of 0.18, 0.25, 0.40, 0.50, 0.625, and 0.75, respectively. 

A comprehensive analysis of the measured atomic ratios in solution during sintering of separate 

nanoparticles is summarized here. Figures 15a and 15b show the normalized amount of 

computed solution ratios by Ni fraction through stage 2 and during stage 3, respectively. 
20 

(a) (b)

Figure 15. The results here show the fraction of Ni in each alloy at stages (a) 1 and (b) 2 versus fraction of all atoms 

in each alloy, i.e., a data point at (0.25, 0.1) corresponds to 10% of all atoms in the system belong to 

Al3Ni. 

During stage 1, from 0 to 50 ps for sintering of 10-nm-diameter particles, most of the atoms 

remain in the pure metal phase, with only a small fraction of atoms, less than 5%, forming Ni 

rich solutions such as Ni3Al. In figure 6a, at 50 ps, an observed peak at 0.75 fraction Ni (Ni3Al) 

is likely due to the shorter bond length of Ni-Ni, such that near the contact interface each Al 

atom will bond with multiple Ni atoms. During stage 2, the formation of Al rich liquid solutions 

occurs at a rapid rate, quickly depleting the atomic fraction of pure Al in the system by the end of 

stage 2 (500 ps). In figure 16a, at 500 ps, a small peak between 0.2 and 0.3 fraction Ni is 

observed, corresponding to Al3Ni. At the end of stage 2, the largest portion of any material is still 

pure Ni (figure 16b). The initial formation of Al rich solutions is supported by experimental 

observations (32, 34). The reaction process that produces these alloys is likely explained by Ni 

atoms diffusing into the liquid Al region forming Al rich clusters of Al3Ni. These clusters then 

diffuse through the Al melt, eventually forming the eutectic mixture. Figure 16b supports this 

process, because small clusters of Al rich alloys are clearly evident in the liquid Al, with some 

initial coalescence of clusters to obtain the eutectic atomic ratio. 

(a)

50 ps 

(b)

500 ps 

Figure 16. Plot showing spatial distribution of Ni fractions during stages (a) 1 and (b) 2 of the sintering process. 
21 

The lines in figure 17b for stage 3 indicate a rapid reduction in the amount of pure Ni and the 

corresponding formation of NiAl. During stages 1 and 2, as observed in figure 3, the temperature 

of the system is rising monotonically. Near the start of stage 3, the system temperature has 

reached the melting point of Ni. At 700 ps, shortly after the Ni nanoparticle has completely 

melted, two peaks are present in figure 17a near 40% Ni and 50% Ni, corresponding to Al3Ni2

and NiAl. In figure 17a, shortly after melting of the Ni nanoparticle, there is a Ni rich region 

visible. This region quickly disappears as the SHS reaction proceeds rapidly to form the eutectic 

alloy. After nearly complete sintering at 950 ps, the majority of atoms are in a NiAl liquid 

solution with some temporal formation of other alloys. This brief analysis has demonstrated that 

the various solution ratios are an interesting problem that warrants closer thermodynamic 

analysis. 

(a)

700 ps 

(b)

950 ps 

Figure 17. Plot showing spatial distribution of Ni fractions at the (a) beginning and (b) end of stage 3 of the 

sintering process. 

8. Conclusions 

We have analyzed two model systems for the energetic reaction of Ni and Al. In the first case, 

we considered the coalescing and sintering of separate nanoparticles and found that the energy 

release from the change in surface area was only significant for small, less that 10-nm-diameter, 

nanoparticles. These separated nanoparticle reaction simulations and thermodynamic analyses 

showed that the reaction time decreased and the adiabatic reaction temperature increased with 

decreasing nanoparticle sizes. This may be important for applications where high energy release 

rates are desired. The simulation data closely matched a classical thermodynamic analysis. 

In the second part of this work, we considered the sintering of Al-coated Ni nanoparticles and 

Ni-coated Al nanoparticles as a model material system for nanoparticles embedded in a matrix of 

the other metal. This work revealed that the reaction time was again inversely related to 

nanoparticle size, but the adiabatic temperature decreased with decreasing nanoparticle size. 
22 

Mechanically, the Al-coated Ni nanoparticle system was a model system for a lightweight Al 

matrix with embedded Ni nanoparticles, a system with relatively high strength compared to a 

loosely bonded powder of Al and Ni nanoparticles. This Al matrix system could be used in 

systems where mechanical strength is important in addition to energy release from kinetic 

sintering of the Ni and Al atoms. In the Ni-coated Al nanoparticle system, we investigated 

possible rupture and fragmentation of the Ni shell but were unable to observe any fragmentation. 
23 

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26 

List of Symbols, Abbreviations and Acronyms 

Al aluminum 

ARO U.S. Army Research Office 

EAM embedded atom method 

LAMMPS Large-scale Atomic/Molecular Massively Parallel Simulator 

MD molecular dynamics 

MSRC U.S. Army Major Shared Resource Center 

Ni nickel 

NiAl nickel aluminide 

NIST National Institute for Standards Technology 

SHS self-propagating high-temperature synthesis 

TB tight-binding 
27 

No. of 

Copies Organization 

 1 ADMNSTR 

 ELEC DEFNS TECHL INFO CTR 

 ATTN DTIC OCP 

 8725 JOHN J KINGMAN RD STE 0944 

 FT BELVOIR VA 22060-6218 

 1 CD OFC OF THE SECY OF DEFNS 

 ATTN ODDRE (R&AT) 

 THE PENTAGON 

 WASHINGTON DC 20301-3080 

 1 US ARMY RSRCH DEV AND ENGRG 

 CMND 

 ARMAMENT RSRCH DEV & ENGRG 

 CTR 

 ARMAMENT ENGRG & TECHNLGY 

 CTR 

 ATTN AMSRD AAR AEF T J MATTS 

 BLDG 305 

 ABERDEEN PROVING GROUND MD 

 21005-5001 

 1 PM TIMS, PROFILER (MMS-P) 

 AN/TMQ-52 

 ATTN B GRIFFIES 

 BUILDING 563 

 FT MONMOUTH NJ 07703 

 1 US ARMY INFO SYS ENGRG CMND 

 ATTN AMSEL IE TD A RIVERA 

 FT HUACHUCA AZ 85613-5300 

 1 COMMANDER 

 US ARMY RDECOM 

 ATTN AMSRD AMR 

 W C MCCORKLE 

 5400 FOWLER RD 

 REDSTONE ARSENAL AL 35898-5000 

 1 US GOVERNMENT PRINT OFF 

 DEPOSITORY RECEIVING SECTION 

 ATTN MAIL STOP IDAD J TATE 

 732 NORTH CAPITOL ST NW 

 WASHINGTON DC 20402 

 1 UNIV OF MARYLAND 

 DEPT OF MECHANICAL 

 ENGINEERING AND THE DEPT OF 

 CHEMISTRY AND BIOCHEMISTRY 

 ATTN M ZACHARIAH 

 2125 GLENN L. MARTIN HALL 

 COLLEGE PARK MD 20742 

No. of 

Copies Organization 

 1 TAKHUMI HAWA 

 218 FELGAR HALL 

 865 ASP AVENUE 

 NORMAN OK 73019-1052 

 1 US ARMY RSRCH LAB 

 ATTN RDRL CIH C B HENZ 

 ABERDEEN PROVING GROUND MD 

 21005 

 1 US ARMY RSRCH LAB 

 ATTN RDRL CIM G T LANDFRIED 

 BLDG 4600 

 ABERDEEN PROVING GROUND MD 

 21005-5066 

 3 US ARMY RSRCH LAB 

 ATTN IMNE ALC HRR 

 MAIL & RECORDS MGMT 

 ATTN RDRL CIM L TECHL LIB 

 ATTN RDRL CIM P TECHL PUB 

 ADELPHI MD 20783-1197 

TOTAL: 14 (1 ELEC, 1 CD, 12 HCS) 
28 

INTENTIONALLY LEFT BLANK.