Powder X-ray diffractometric analysis has been performed to assess the crystallographic phase stabilities of the title materials. As seen in Fig. 1a, it is noticed that the control test sample has the anatase phase which is very much evident from the high intensity characteristic peak (101) at the diffraction angle 25° . In addition to that, it has some minor diffraction peaks at 41.26°, 62.63°, 64.68° which belong to the rutile phase. While considering the rutile phase, the corresponding diffraction planes are (110), (101), (200), (111), (210), (211), (220), (002), (310), (301), and (112). The observed XRD pattern is well-matched with ICDS data base code number 9161 and the corresponding XRD pattern is presented in Fig. 1b. At shock wave loaded conditions, there is no significant change observed up to 60 shocks in terms of peak shift and peak broadening of (101) whereas at 90 shocks, the mother phase of the test sample is turned into the rutile phase by the impact of shock waves and the observed phase sequence with respect to number of shock waves is well consistent with our previous observation . There are number of valid reasons behind the transition of the anatase to rutile phase at shocked conditions that are prerequisites so as to understand better the shock wave induced phase transition. As the possible scientific reasons behind the particular phase transition are analyzed, it is found in the literature that the crystallographic parameters of the anatase phase are a = 3.785, b = 3.785, and c = 9.514 Å and it has the tetragonal crystal structure . The anatase phase has significantly longer c-axis than that of both a and b axes so that c-axis has more compressibility than the other two axes and it can be considered as a prominent key point for the occurrence of the phase transition. On the other hand, the anatase phase has octahedral population which has hard occupied (TiO6) and soft empty (O6) sites [30, 31].
Hence, there are plenty of possibilities for the anatase phase to be changed into another phase which is controlled by the external parameters such as pressure and temperature. During the shock wave loaded conditions, the c-axis may break along its length in-local coordination bond network especially the bonds between Ti − O (1) and Ti − O (2) of anatase which in turn trigger the formation of next possible phase of the mother compound. Moreover, during the bond breakage of the anatase TiO2 NPs that are formed along with the c-axis could suffer significant volume reduction or compression caused by the impact of shock waves. Hence at this stage, the rutile phase has to be the next possibility to occur due to the impact of shock waves. Since rutile belongs to the tetragonal phase (P42/mnm), the geometrical values are a = 4.593, b = 4.593 and c = 2.959 Å [30, 31]. During the shock wave loaded condition, the anatase phase has experienced significant reduction of length in c-axis whereas slight enhancement is observed for a and b-axes so that the rutile phase has emerged at the shocked conditions. Moreover, the required time is highly dependent on the values of transient pressure and temperature with which the anatase to the rutile phase transition has been achieved at 90 shocks. But in the case of the rutile phase, following with the same number of shocks and the same interval i.e., from 0 to 90 shocks, neither peak shift nor phase change have been observed. The zoomed versions of the XRD patterns are presented in Fig. 2 for better visibility. Based on the observed results, it is quite clear that, the anatase phase is less stable than that of the rutile phase which is well consistent with the reported thermodynamic stability profiles .
While considering the crystal structure of rutile, it belongs to the tetragonal unit cell having titanium cations and oxygen anions. The coordination numbers of the titanium cations and oxygens are six and three, respectively. It could be noted that the local structure of TiO6 octahedron which give rise to the basic building unit has the resemblance as in the rutile and anatase, whereas the connection existing between the neighboring TiO6 octahedra is not the same for both the phases. To be more specific, every TiO6 octahedron found in anatase is connected to 8 neighboring octahedra (four by edge sharing and four by corner-sharing) while each TiO6 octahedron in rutile has the connection of 10 neighboring octahedra (two by edge sharing, and eight by corner-sharing) . The sharing edges of the TiO2 may lead to the high shock resistance of the rutile – TiO2 at shocked conditions. As seen in Fig. 2b, the characteristic diffraction peak position of the rutile phase (110) remains the same with respect to the number of shock pulses and the shape of the diffraction peak is not changed. It is a key point to be considered for high shock resistant materials. On the other hand, while looking at the actual crystal structure of the rutile, the adjacent distance between Ti atoms is significantly lower as compared to the anatase. As seen in Fig. 3, the length of adjacent Ti atoms and bond angle is significantly low compared to the anatase phase. As mentioned above, the rutile phase has a more closely packed crystal structure as compared to the anatase as well as the gap between the most occupied (valence band) state and the least occupied (conduction band) state. The structural features of the rutile phase with lower k value enables the interactions stronger that occur between Ti-3d and O- 2p which give rise to significantly higher band dispersion in the rutile phase than that of the anatase [32, 33]. So that, the interaction between Ti-O-Ti is much higher than that of the anatase phase that may also lead to acquire high shock resistance. In addition to that, in the case of TiO2, the values of surface energy of the anatase (101) and rutile (110) phases are found to be 0.51 Jm− 2 and 0.60 Jm− 2, respectively [32, 33]. Based on the crystallographic point of view and chemical point of view, the rutile phase TiO2 has a highly favorable crystal structure configuration than that of the anatase phase and also high shock resistant behavior so that the rutile-TiO2 can be a potential material for the applications of device fabrication. Figure 4 provides the possible mechanism of the crystal phase transitions form the anatase to the rutile phase at shocked conditions.
As seen in Fig. 4, the horizontal Ti-O bonds might have broken at 90 shocked conditions so as to form the rutile phase TiO2 that are marked in ellipsoids in Fig. 5. But there is no crystallographic and lattice deformation that is found for the rutile TiO2 at shocked conditions. Furthermore, as seen in Fig. 2a and Fig. 3a, there is considerable signature of the anatase phase in the shock wave induced rutile phase. The percentage of the presence of the anatase and the rutile phases at 90 shocked conditions is calculated using standard formulation .
During the shock wave induced phase transition of the anatase to the rutile, the anatase phase is not completely converted to the rutile phase wherein the respective ratio of the phases are 9.173 % and 90.827 % for the anatase and the rutile phase at 90 shocked conditions. In the case of rutile, no change is found.