Shock Induced Chemical Reactions of Intermetallic Mixture of Nickel and Aluminum and Associated Transition States

In this paper, numerical simulation of shock-induced chemical reactions of intermetallic mixtures is discussed. Specifically, the paper focuses on intermetallic mixture of nickel and aluminum. To initiate the chemical reactions, the thermal input or the shockwave should supply the energy to take the reactants, mixture of nickel and aluminum, to the transition state. Thus, for any numerical simulation or analysis of the shock or thermally induced chemical reaction in a continuum scale or a meso scale, it is necessary to identify the transition state. The transition state for the intermetallic mixture of nickel and the aluminum is identified in this paper and a result of the numerical simulation of the shock-induced chemical reaction, in a continuum scale is presented. The numerical solutions clearly show the chemical reactions, release of heat energy, increase of the temperature and the formation of products, following the transition state and the resulting shock-induced chemical reaction of a binary intermetallic energetic mixture of nickel and aluminum. The studies also show that the collapse of porosity is a mechanism that takes the reactants to the transition state, in shock-induced chemical reactions of binary intermetallic mixtures.

HMX. The second class of energetic materials is known as reactive materials and has two sub-categories. The first category consists of mixtures of metal and metal oxide. The second sub-category consists of an intermetallic mixture of metals.
These intermetallic mixtures offer high mixture density, with the potential to release a significant amount of heat energy, following the chemical reaction. The high density is also associated with high tensile strength and high structural strength. Thus, some of these intermetallic mixtures are ideally suited for dual functional structural-energetic materials. To illustrate, the following table displays a few selected intermetallic mixtures, the associated mixture densities, reaction temperatures and potential release of heat energy [2]. To understand the shock-induced chemical reactions theoretically, it is necessary to formulate equations of motion, including the conservation of mass, conservation of energy, nonequilibrium thermodynamics equations, transition states and associated chemical reaction equations. Then, it is also necessary to formulate procedures for numerical simulation of shock-induced chemical reactions and analyze the results. Such a numerical simulation requires procedures to identify the transition states. The objectives of this paper are to illustrate the needed procedures to find transition states in intermetallic mixtures. Because of the availability of the needed literature [3] [4], the intermetallic mixture of nickel and aluminum is selected for finding the transition states and presents a numerical study of the shock-induced chemical reaction.

Transition State
There are theoretical and experimental studies to understand the reaction me- We know the reactants and products, but we do not know the transition state.
Thus, prior to any numerical simulation of shock-induced chemical reactions, it is necessary to determine the transition states.
The next steps of discussions consider the explanations of the term transition state. If we place nickel and aluminum particles on a table at room temperature, in contact with each other, no reactions take place unless we supply some energy to initiate the reaction. This energy that we supply and is sufficient to initiate the reaction is known as the transition state energy. This transition state energy is higher than the energy associated with the reactants, nickel and aluminum, and the product nickel-aluminide. At the transition state, we may have a transition state product that is different from nickel, aluminum or nickel-aluminide.
Studies in transition states are still an active research area [5]. A significant experimental contribution to this field is by Zewail [6]. In this paper, a method is presented to identify transition states for the shock-induced chemical reaction of the intermetallic mixture of nickel and aluminum. The approach is not experimental. The presented procedure is a theoretical method, similar to the method of reference [7].

Identification of Transition States for the Shock Induced Chemical Reactions of the Intermetallic Mixture of Nickel and Aluminum
Of the two components of the mixture, aluminum has a lower melting temperature and hence the chemical reaction initiation criteria are based on the melting temperature of aluminum. The reaction between nickel and aluminum can give The transition state of both these reactions needs to be identified. The procedure followed is that applied for the thermite mixture [7]. Various compounds that are formed from a stoichiometric composition of nickel and aluminum are identified from the chemical database. The Gibbs free energy of these compounds is then compared. The energy of the transition state must be greater than the energy of both the reactants and products. At the same time, given two possibilities, the one with the lower energy is selected as the transition state. This is because this state would require less supply of energy for the reaction to occur and hence has a high probability of being the transition state of the reaction.
Using these guidelines, the possible transition species for Equation (2)  where "s" refers to the solid state and "l" the liquid state. The possible reaction path using these transition species are as follows: Ni 3Al Ni l 3Al l NiAl Ni 3Al Ni l 3Al s NiAl Ni 3Al Ni s 3Al l NiAl Ni 3Al NiAl s 2Al s NiAl Ni 3Al NiAl s 2Al l NiAl Ni 3Al NiAl l 2Al s NiAl Ni 3Al NiAl l 2Al l NiAl Ni 3Al 0.33Ni Al s 2.67Al l NiAl Ni 3Al 0.33Ni Al s 2.67Al s NiAl Ni 3Al 0.33Ni Al l 2.67Al s NiAl Ni 3Al 0.33Ni Al l 2.67Al l NiAl + = + = The Gibbs free energy for each of these transition states is plotted in Figure 2 3Ni Al NiAl l 2Ni s Ni Al 3Ni Al NiAl l 2Ni l Ni Al 3Ni Al 0.33NiAl s 2.67Ni l Ni Al 3Ni Al 0.33NiAl s 2.67Ni s Ni Al 3Ni Al 0.33NiAl l 2.67Ni s Ni Al 3Ni Al 0.33NiAl l 2.67Ni l Ni Al + = + = Figure 3 depicts the Gibbs free energy of the transition states along with the reactants and product. Comparison of the energies determines the transition state for the reaction to be Ni(l) + Al(l).

Shock or Impact Induced Reactions with Identified Transition States
The transition state and the activation energy for the chemical reaction between the mixture of aluminum and nickel have been identified. The mixture equation of state obtained from the species equation of state has been derived. This equation has also been validated for accuracy. The next step is to analyze the In Figure 4, the variation of the temperature, the formation and the concentration of the product NiAl 3 for different impact velocities are illustrated. As the impact velocity increases from 500 m/s to 1500 m/s, the temperature in the system increases. Consequently, the reaction rate increases and the concentration of the product increases. It can also be observed from the figure that once the reaction goes to completion at a particular region, a further increase in temperature does not have any more effect on the reaction process. As the impact velocity increases, more regions of the specimen have a temperature beyond the reaction initiation temperature and hence the reaction process is seen to move spatially into the specimen.   is increased to take the reactants to the transition state. As the porosity in the system increases from 0 to 30%, the temperature in the system increases and consequently, the reaction rate increases and thus, the product concentration increases.

Conclusion
In this paper, we have developed a procedure to determine the transition states for shock or impact-induced chemical reactions of binary energetic materials that are also known as reactive materials. Specifically, the transition states are theoretically obtained for intermetallic mixtures of nickel and aluminum that offer dual functions of structural strength and the capability to release heat energy, following the shock-induced chemical reaction. The derived transition states are then used to study, numerically, the shock-induced chemical reactions, by the use of the mixture theory, conservation equations in the framework of nonequilibrium thermodynamics and modified chemical reaction equations. Effects of varying impact velocities that result in the varying shock velocities are studied. Then, the effect of initial porosity on the shock-induced chemical reactions is studied. The presented numerical studies, on the binary mixture of nickel and aluminum, clearly show the reactions that follow the transition states. The numerical studies also indicate that pore collapse as one of the mechanisms takes the reactants to the transition state, during the shock or impact effect on binary energetic reactants. The methods presented in this paper can be used to study V. Narayanan, S. Hanagud