Numerical analysis of atomic motion in the incommensurate phase of quartz (SiO ₂ ) in the vicinity of phase transition

Abstract

In order to find out the details of microscopic structure of incommensurate (IC) phase in quartz, we studied numerically the time correlation in the atomic motion and the static pattern of the structure at different temperatures. The analysis of temperature dependence of the numerical data revealed several important facts, which strongly support the recent theoretical assumptions concerning the possibility to observe IC phase in quartz and concerning geometrical interpretation of the neutron diffraction pattern.

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

“…The solution (35), as can be seen from a comparison with the solution for a four-period structure (34), suggests that the soliton gradually changes the phase of the four-period structure. We can also construct a different solution, assuming a gradual change of the functions 4n u , 4 1 n u + , 4 2 n u + and 4 3 n u + .…”

“…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].…”