Chapter 3
Vibrational Up-Pumping: Predicting
Impact Sensitivity of Some Energetic
Azide
3.1 Introduction
To a simple approximation, a mechanical impact can be taken to induce two main
effects: (1) the material being impacted is compressed, and (2) if the impact energy
exceeds a threshold energy, fracture of the impacted body [3]. In the first, a compressive pressure wave passes through the material, akin to an acoustic wave. The propagation of this pressure wave through the material has been suggested to induce
vibrational excitation of the lattice by a two-fold mechanism [4]. The pressure associated with the impact leads to a shift in the vibrational frequencies of the material.
These vibrations are subsequently populated by the sudden increase in energy of the
lattice. For the adiabatic compression of a solid [5],
T
T o
=
V
V o
−Γ
(3.1)
where G is the Grüneisen parameter describing the vibrational anharmonicity of the
lattice, V/V 0 describes the change in volume on compression, and T/T 0 is the change
in temperature of the bulk material on compression. The exact temperature that can
be achieved depends largely on the heat capacity of the material [6]. It follows that
the magnitude of the excitation that results from an impact is proportional to the
magnitude of the impact pressure, and the response of the material to this pressure
[7–9].
Previous work found that for the model organic material naphthalene, a modest
impact (4 GPa) is associated with a total increase in internal energy, U, of
37,000 cm
−1 per molecule [6]. However, as U = H + W, the increase in internal
energy will distribute between heat (H) and work (W ). The proportion of U that
converts to H follows from Eq. 3.1, and therefore increase with the anharmonicity
Parts of this chapter have been reproduced with permission from Ref. [1] Copyright 2018 American
Chemical Society, and Ref. [2] CC BY 3.0.
© Springer Nature Switzerland AG 2020
A. A. L. Michalchuk, Mechanochemical Processes in Energetic Materials,
Springer Theses, https://doi.org/10.1007/978-3-030-56966-2_3
65
Vibrational Up-Pumping: Predicting
Impact Sensitivity of Some Energetic
Azide
3.1 Introduction
To a simple approximation, a mechanical impact can be taken to induce two main
effects: (1) the material being impacted is compressed, and (2) if the impact energy
exceeds a threshold energy, fracture of the impacted body [3]. In the first, a compressive pressure wave passes through the material, akin to an acoustic wave. The propagation of this pressure wave through the material has been suggested to induce
vibrational excitation of the lattice by a two-fold mechanism [4]. The pressure associated with the impact leads to a shift in the vibrational frequencies of the material.
These vibrations are subsequently populated by the sudden increase in energy of the
lattice. For the adiabatic compression of a solid [5],
T
T o
=
V
V o
−Γ
(3.1)
where G is the Grüneisen parameter describing the vibrational anharmonicity of the
lattice, V/V 0 describes the change in volume on compression, and T/T 0 is the change
in temperature of the bulk material on compression. The exact temperature that can
be achieved depends largely on the heat capacity of the material [6]. It follows that
the magnitude of the excitation that results from an impact is proportional to the
magnitude of the impact pressure, and the response of the material to this pressure
[7–9].
Previous work found that for the model organic material naphthalene, a modest
impact (4 GPa) is associated with a total increase in internal energy, U, of
37,000 cm
−1 per molecule [6]. However, as U = H + W, the increase in internal
energy will distribute between heat (H) and work (W ). The proportion of U that
converts to H follows from Eq. 3.1, and therefore increase with the anharmonicity
Parts of this chapter have been reproduced with permission from Ref. [1] Copyright 2018 American
Chemical Society, and Ref. [2] CC BY 3.0.
© Springer Nature Switzerland AG 2020
A. A. L. Michalchuk, Mechanochemical Processes in Energetic Materials,
Springer Theses, https://doi.org/10.1007/978-3-030-56966-2_3
65