3.5 Results and Discussion
101
describing the sensitivity ordering of these materials. This deficiency is particularly notable for the low sensitivity materials and HN 3 . However, in developing the
up-pumping model, interest rests in the localisation of energy. Hence, it is worth
recasting these values based on the number of molecules present in the unit cell (this
also has the effect of correcting for the use of conventional cells in some cases),
Fig. 3.20c. Renormalisation in this manner highlights even further the deficiencies
of considering only overtone pathways in the up-pumping model, with HN 3 in particular being substantially underestimated in its sensitivity. The general trend remains
with sensitive compounds exhibiting higher integrated overtone densities than the
less sensitive compounds.
Multiphonon Density of States: Combination pathways
Given the deficiency of the overtone pathways alone, it was necessary to consider
also the combination pathways. This was done by generation of
(2) for each of the
materials under investigation, Fig. 3.21. By Eq. 3.5, only up-conversion processes are
accounted for, ensuring ω q j and ω q j < ω T . To further adhere to the model proposed
in Sect. 3.5.3, further constraints are imposed on generation of
(2) , ensuring that
ω q j and ω q j < 2
(2) and ω q j < < max . This ensures that all values of
(2)
<
3 max must include at least one phonon mode. It is generally found, however, that
this restriction has little effect on the structure of
(2) (ω T ), Fig. 3.21. Generally, it is
found that ω T falls within the region of this restricted
(2) for the sensitive materials,
with little to no
(2) density found at ω T for insensitive materials. The magnitude
of
(2) is seen to increase notably with increasing sensitivity. Only one exception
(Ba(N 3 ) 2 ) is found to this trend. Despite its similarity to the PDOS of AgN 3 , the
lower value of max for Ba(N 3 ) 2 means that the ω T sits just beyond the doorway
region. Thus, the magnitude of
(2) in the restricted case is necessarily zero, given
no doorway modes are present. The calculated G-point max of Ba(N 3 ) 2 agrees well
with experimental measurements (230−240 cm
−1 ) [98] and suggests minimal error
in the selection of the phonon bath for this material.
Prediction of Impact Sensitivity
By imposing the approximation that ω T is flat (i.e. q-invariant), the total value of
(2) (ω T ) is indicative of the number of coupling pathways capable of up-converting
energy into this mode. Based on Eq. 3.5, it follows that the faster energy can transfer
into ω T , the lower the dissipation of this energy and the more sensitive will be the
compound.
A clear correlation is observed between
(2) (ω T ) and the experimental impact
sensitivity for each compound, Fig. 3.22. The insensitive materials exhibit
(2)
(ω T ) ≈ 0. This suggests that within the ideal crystal, direct transfer of energy into
ω T is not possible, and therefore that they cannot be easily initiated by impact. The
calculated value of
(2)
(ω T ) increases with increasing experimental impact sensitivity. However, by enforcing ω q j and ω q j < 2 max and ω q j < < max , Ba(N 3 ) 2
appears to be as insensitive as α-NaN 3 , Fig. 3.22a. If this restriction is lifted and
consideration is therefore given to all combination modes (ω q j and ω q j < ω T ),
the predicted sensitivity of Ba(N 3 ) 2 increases in line with the sensitive materials,
101
describing the sensitivity ordering of these materials. This deficiency is particularly notable for the low sensitivity materials and HN 3 . However, in developing the
up-pumping model, interest rests in the localisation of energy. Hence, it is worth
recasting these values based on the number of molecules present in the unit cell (this
also has the effect of correcting for the use of conventional cells in some cases),
Fig. 3.20c. Renormalisation in this manner highlights even further the deficiencies
of considering only overtone pathways in the up-pumping model, with HN 3 in particular being substantially underestimated in its sensitivity. The general trend remains
with sensitive compounds exhibiting higher integrated overtone densities than the
less sensitive compounds.
Multiphonon Density of States: Combination pathways
Given the deficiency of the overtone pathways alone, it was necessary to consider
also the combination pathways. This was done by generation of
(2) for each of the
materials under investigation, Fig. 3.21. By Eq. 3.5, only up-conversion processes are
accounted for, ensuring ω q j and ω q j < ω T . To further adhere to the model proposed
in Sect. 3.5.3, further constraints are imposed on generation of
(2) , ensuring that
ω q j and ω q j < 2
(2) and ω q j < < max . This ensures that all values of
(2)
<
3 max must include at least one phonon mode. It is generally found, however, that
this restriction has little effect on the structure of
(2) (ω T ), Fig. 3.21. Generally, it is
found that ω T falls within the region of this restricted
(2) for the sensitive materials,
with little to no
(2) density found at ω T for insensitive materials. The magnitude
of
(2) is seen to increase notably with increasing sensitivity. Only one exception
(Ba(N 3 ) 2 ) is found to this trend. Despite its similarity to the PDOS of AgN 3 , the
lower value of max for Ba(N 3 ) 2 means that the ω T sits just beyond the doorway
region. Thus, the magnitude of
(2) in the restricted case is necessarily zero, given
no doorway modes are present. The calculated G-point max of Ba(N 3 ) 2 agrees well
with experimental measurements (230−240 cm
−1 ) [98] and suggests minimal error
in the selection of the phonon bath for this material.
Prediction of Impact Sensitivity
By imposing the approximation that ω T is flat (i.e. q-invariant), the total value of
(2) (ω T ) is indicative of the number of coupling pathways capable of up-converting
energy into this mode. Based on Eq. 3.5, it follows that the faster energy can transfer
into ω T , the lower the dissipation of this energy and the more sensitive will be the
compound.
A clear correlation is observed between
(2) (ω T ) and the experimental impact
sensitivity for each compound, Fig. 3.22. The insensitive materials exhibit
(2)
(ω T ) ≈ 0. This suggests that within the ideal crystal, direct transfer of energy into
ω T is not possible, and therefore that they cannot be easily initiated by impact. The
calculated value of
(2)
(ω T ) increases with increasing experimental impact sensitivity. However, by enforcing ω q j and ω q j < 2 max and ω q j < < max , Ba(N 3 ) 2
appears to be as insensitive as α-NaN 3 , Fig. 3.22a. If this restriction is lifted and
consideration is therefore given to all combination modes (ω q j and ω q j < ω T ),
the predicted sensitivity of Ba(N 3 ) 2 increases in line with the sensitive materials,