Structural mechanics from nonlinear optics – the α to β phase transition in quartz

Abstract

Second harmonic generation SHG may be used as an experimental technique in structural crystallography. By applying a bond polarizability model to the nonlinear optical coefficients of quartz, the rotation of the SiO4 tetrahedron with temperature is "observed'. Additionally, the oxygen positional parameter x in /3 quartz is obtained in excellent agreement with previously published X-ray results.

Calculation of Bond Parameters and of Nonlinear Optical Susceptiabilities in Quartz‐Homeotypic MXO4 Crystals

“…Their variations with T are related with the movement of the MO, and XO, tetrahedra, which can be described as the 'back tilting' towards the prototypic P-phase. Quite similar to quartz [27], Gt;,, is an odd function of the tetrahedral angles and is nearly insensitive to other structural changes (e.g. the tetrahedral distortions).…”

“…the tetrahedral distortions). The crystals exhibiting a-P phase transitions (quartz, AlPO,, and FePO,), are characterized by the completion of the tilting motion of tetrahedra to zero tilt angles (in quartz, dSio4 decreases from 16" at RT to zero at 846 K [27]; in AlPO,, 6A,04 and BPo4 decrease from about 19" and 17", respectively, at RT to zero above 858 K [26]). Thus Gt; ,, d, ,, and A , are zero in the P-phase.…”

“…The results of the evaluation of (17) to (27) are shown in Table 1 (for G,,,), Table 4 (the last two columns), and Table 5. Table 4 Linear and nonlinear bond susceptibilities of quartz-homeotypic crystals …”

“…(28) to (30), the nonlinear bond properties are obtained by exploiting (17) to(27) and taking r : -O = 0.59rF-O, which results analogously to Cu[23] from the geometrical average r: = ((rc)Fe (rc)Ox)1'2 (31) using (r,)Fe x ro and Since Fe in FePO, is in its trivalent state, one of the d electrons contributes to the bond charge through nva, = 15/4 as given in Table2. The other d electrons contribute to the bond charge indirectly through their influence on x and f,(21).…”

The Temperature Dependence of the Optical Second Harmonic Generation Coefficient d11 of Quartz Homeotypic AlPO4 (Berlinite)

“…The difference between the two phases mainly lies in the mean rotation angles of the A10, and PO, tetrahedra, which are zero in the P-phase and increase to about 6A,04 E 16" and BPo4 E 19" [25] upon cooling to ambient temperatures. Since, quite similar to quartz [26], GE, is an odd function of the tetrahedral angles and is nearly insensitive to other structural changes (e.g. the tetrahedral distortions), any changes in 6 will affect GE , (which is zero in the /?-phase), and therefore influence dijk.…”