Structure de la phase ferroélectrique–ferroélastique du tanane (diffraction neutronique). Evaluation d'energies de réseau

Abstract

The structure of the ferroelectric-ferroelastic phase of 2,2,6,6-tetramethylpiperidine 1-oxyl (C9HlsNO, 'tanane') was refined from neutron diffraction data [a = 22.64 (2), b = 21.71 (2), c = 8.030 (6) ,/k, Faa2, z = 16, 1022 observed reflections, 262 parameters, R w = 0.06]. The crystal was kept as a single domain by a uniaxial constraint. Little structural change was observed with respect to the tetragonal disordered hightemperature phase. Results of empirical calculations of electrostatic and van der Waals intermoleeular energies for the three forms of tanane are in agreement with their domains of stability.

A Radical Approach to Hydroxylaminotrichlorosilanes: Synthesis, Reactivity, and Crystal Structure of TEMPO‐SiCl3 (TEMPO = 2,2,6,6‐Tetramethylpiperidine‐N‐oxyl)

“…The N-O bond lengths found in these studies are 1.269, 1.270, and 1.295 Å. [31][32][33] In the course of our investigations we have been able to obtain crystals of TEMPO by sublimation with excellent quality for X-ray diffraction. The structure could be solved and refined with an R 1 value of 3.8 % and no disordered atoms.…”

Ferroelastic and ferroelectric phase transition in a molecular crystal : tanane - 3. — From ab initio computation of the intermolecular forces to statistical mechanics of the transition

“…So we conclude that without accurate determination of the actual hydrogens positions, the approximation proposed by E. Giglio may yield better results than the detailed analysis proposed by K. Mirsky. In addition, it is confirmed [14] that the simulation of a strained lattice performed by just changing the lattice parameters remains valid for strains lower than 5 x 10-2 (especially for the calculation of the elastic moduli) although in such a simulation both the intermolecular distances (van der Waals interactions) and the intramolecular distances (covalent bonds) are changed in a similar way.…”

“…The sums performed in table I show that, in the « rigid » tetragonal lattice : Y Bij = 0 (in agreement with the symmetry) . j Thus, the Hamiltonian Je separates into a pure « lattice » part : Y Aij, which represents the van der j Waals cohesion energy, per molecule, in the disordered phase [14] ; and an Ising part : si Y-si Jij, for j which there is no exact solution in case of 3-d Ising model. Thus we simply use the « mean-field » approximation which yields for the ordering temperature of the pseudo-spin system : Especially this last prediction appears to be in remarkable agreement with the transition temperature of the « damped » crystal deduced from the (mean-field) analysis of the experimental results [111 : However, the ordering temperature given by the « mean-field» approximation should be higher than the actual transition temperature, because this approximation does not take into account the effects of the fluctuations [10].…”

“…Also the calculated interaction energies appear rather sensitive to slight changes in the intramolecular distances [20]. Thus, following the usual procedure [18], we use standard interatomic distances for the C-H bonds (1.08 A) instead of those determined with poor accury from neutron diffractometry [14].…”

“…If we now consider the permanent dipole moments of the molecules oriented along the N-0 bond and estimated to be : J.l = 3.14 Debyes from measurements in solutions [13], and p = 2.95 Debyes from calculations of the electronic density [14], the spontaneous polarization Pz of the completely ordered crystal can be estimated from structural data to be :…”