# ZIF-75 under Pressure: Negative Linear Compressibility and Pressure-Induced Instability
## 4 Discussion  
The elasticity matrix of ZIF-75 was determined at the equilibrium crystal structure employing the FDM technique. The study of the mechanical stability of ZIF-75 showed that it is unstable. The reason for the mechanical instability of ZIF-75 was unveiled by the examination of the variation of the computed crystal structures under the effect of pressure, showing that ZIF-75 undergoes a pressure-induced phase transition at very small applied pressures of \(P\approx 0.1\) GPa. Furthermore, the study of the variation of the unit cell parameters under pressure showed that the behavior of the \(c\) lattice parameter is anomalous. It strongly increases in the pressure range from \(P=-0.06\) to 0.1 GPa; therefore, ZIF-75 presents the negative linear compressibility phenomenon in this range of pressure. The modifications of the crystal structures were analyzed in order to study the structural mechanism leading to the presence of the phenomenon of negative linear compressibility. The inspection of the deformation of these structures as the pressure increases led to the conclusion that the NLC phenomenon in ZIF-75 can be understood by employing the empty channel structural mechanism [81; 82; 83; 128]. The modifications of the structure of ZIF-75 at four different pressures, \(P=-0.0625\), 0.0, 0.0625, and 0.125 GPa, are shown in Figure 6.  
Figure 6: View of crystal structure of ZIF-75 from [1 0 0] crystallographic direction at four different pressures, \(P=-0.0625\), 0.0, 0.0625, and 0.125 GPa. The subfigure corresponding to \(P=0.125\) GPa provides a view of the crystal structure after the pressure-induced phase transition. Color code: Zn—green; N—blue; C—gray; O—red; H—white. In microporous materials exhibiting empty structural channels, the application of isotropic pressure may lead to a flattening of the channels which become wider along the direction of the largest semiaxis in a section perpendicular to the channels and shorter in the perpendicular direction. The widening of the channels in turn leads to the increase in the corresponding lattice parameter, which in the present case is the \(c\) lattice parameter. This mechanism, described for the first time in 2020, has been found to be responsible for the NLC phenomenon in several different microporous materials [81; 82; 83; 128]. The last crystal structure of ZIF-75 shown in Figure 6, corresponding to an applied pressure of \(P=0.125\,\mathrm{GPa}\), is, as expected, completely different from the other ones because this pressure is well beyond the phase transition pressure. In this structure, the presence of smaller structural empty channels expanding along the [0 0 1] direction is still observed. The new material generated through the pressure-induced transition must have completely different properties to those of ZIF-75 and may be functional for other applications. The reversibility of the phase transition upon the removal of the effect of pressure and properties of the new material should be experimentally investigated in detail. A large set of ZIF materials were selected for this study, such as those synthetized by [PERSON] et al. [1] and [PERSON] et al. [2]. We were looking for microporous materials exhibiting large empty structural channels, which, according to previous studies [81; 82; 83; 128], are likely to exhibit the negative linear compressibility phenomenon. Due to the large size of its structural channels, ZIF-75 was selected among the studied ZIF materials. Therefore, it was a good candidate for the study of its behavior under pressure. Furthermore, the initial exploratory test calculations of this material showed that, indeed, its behavior under pressure was very interesting. For comparison, as far as we know, a pressure-induced instability was only found for the ZIF-8 material [11; 29; 30; 32; 38; 44] at about 0.34 GPa [29], which has long been investigated. The behavior of ZIF-75 material under pressure has never been investigated experimentally.