Commensurately modulated structure of thiourea at 170 K

Abstract

The ninefold superstructure of SC(NHz) 2 was determined by single-crystal X-ray diffractometry at 170 K; orthorhombic, Pbnm, a = 5.467 (1), b = 7.545 (1), c=76.867(I1) A, V=3171.1A 3, Z=36, Dx= 1.435 Mg m -3, Cu K~t, 2 = 1.5418 A, ~ = 5.89 mm-', R=0.048 for 1510 independent reflections. The commensurate phase is stable between the ferroelectric phase (I) and the incommensurate phase (II), in a temperature range of about 2 K. The structure is characterized by a rotation of the SC(NH2) 2 molecule along the c axis coupled with a displacement of the center of mass in a plane perpendicular to the axis. Around mirror planes (z = ¼ or 2) the local structure is isostructural with phase I. Therefore the superstructure is constructed of alternately polarized layers which are sandwiched by domain walls (or discommensurations) whose local structure is that of the paraelectric room-temperature phase (V) around z = 0 and ½. AbstractTwo recent attempts to derive quantitative energy relationships from statistical analysis of structural parameters observed in different crystal environments are examined. Both are based on the assumption of a Boltzmann-like distribution for the probability of a 0108-7681/88/040445-04503.00 structure being observed in a deformed state. This assumption is shown to be untenable. An alternative model taking explicit account of the perturbing forces responsible for structural deformation is then considered. Although low-energy regions of molecular potential energy surfaces can certainly be recognized and mapped from distributions of observed structures,

Mode crystallography of distorted structures

“…Summary of the mode decomposition of the threefold lock-in phase of K 2 SeO 4 (Yamada et al, 1984). , 1989) and as a conventional superstructure (Tanisaki et al, 1988). The two models were shown to be approximately equivalent (Perez-Mato, 1991) (see below).…”

“…Table 18 shows the polarization vector of the primary DT4 distortion in the mode description. The sinusoidal function so defined, together with the modulation wavevector, is sufficient to describe the displacements of the equivalent atoms in the nine Table 18 Reference structure and polarization vector of the (0, 1/9, 0) DT4 distortion in the ninefold Pnma phase of thiourea according to the structure reported as model 1 of Tanisaki et al (1988) Table 17 Summary of the mode decomposition of the ninefold phase of thiourea according to the structure reported as model 1 in Tanisaki et al (1988) (H atoms not included). The three cations S, C and N have a single independent site in the parent unit cell and are split into five, five and nine independent sites, respectively, in the ninefold structure.…”

Structural changes of thiourea in connection with its phase transitions: reappraisal of rigidity and libration of the molecule

“…The structure of the modulated phases has been studied by many workers (Shiozaki, 1971;McKenzie 1975;Takahashi, Onodera & Shiozaki, 1987Gao, Gajhede, Mallinson, Petricek & Coppens, 1988;Tanisaki, Mashiyama & Hasebe, 1988;Simonson, D6noyer, Currat & Vettier, 1988;Zufiiga, Madariaga, Paciorek, P6rez-Mato, Ezpeleta & Etxebarria, 1989). In the works of McKenzie (1975), Takahashi et al (1987Takahashi et al ( , 1988, Gao et al (1988) and Simonson et al (1988), the molecule of thiourea is 0108-7681/90/050661-04503.00…”

Time Relaxation of the Low-Temperature Modulated Structure of Thiourea

“…the same value of ns). Such strict regularity is not exactly true: Among the six modulation functions obtained in a rigid-body approximation of the molecule, there is one that remains almost sinusoidal, the one corresponding to the translation along the a axis (Zfifiiga et al, 1989;Tanisaki, Mashiyama & Hasebe, 1988). The reason for this exception is well understood (Aramburu, Madariaga & Perez-Mato, 1994) but for simplicity this feature has been neglected in the calculations above.…”

“…It will be shown that the time evolution of the reflections can be fully explained in terms of a certain variation of the form of the structural modulation. The previous knowledge of the incommensurate structure determined (Zfifiiga et al, 1989;.Tanisaki, Mashiyama & Hasebe, 1988) and the assumption that the structural modulation approximately satisfies the sine-Gordon equation (Aramburu, Madariaga & Prrez-Mato, 1994, 1995 has been essential for a successful quantitative analysis of the results. The present study demonstrates that, when properly chosen and analysed, check reflections can provide a direct insight of the time relaxation of IC modulations.…”