Simulation of Modulated Structures in Quartz

Long-period states of a crystal finite-size-particle system

“…While such an analysis is quite straightforward, it is not undertaken here since for the respective structures of the period ∞ , 2, 3, 4 and 6 exact solutions have been already described above. A solution of (24), (27) gives a quite exact result for А 1 = 0.1, but even for 1 0.5 A = , when as an example the structures with 2 / 5 k = and are used 20 / 51 k = , we can establish that the difference between the energy of the approximated solution (24) and that of the exact solution (numerical) is found to be about 0.5% . For А 1 = 1 and larger values of the amplitude of the solution, a significant role belongs to the higher harmonics, and the sine mode transforms into that of domain walls, as shown in Fig.…”

“…Reciprocal rotation of tetrahedrons plays an important role in the α-β-phase transition via the incommensurate phase and formation of acoustic properties in quartz in the vicinity of this transition [17][18][19][20]. In the course of analyzing the results obtained on quartz [25][26][27][28][29][30][31][32][33][34] an assumption was made concerning the existence of a relationship between the major effects and the rotational degrees of freedom [35,36].…”