Crystal structures

Abstract

A personal view is offered on various solved and open problems related to crystal structures: the present state of reconstructing the crystal electron density from X-ray diffraction data; characterization of atomic and molecular motion from a combination of atomic displacement parameters and quantum chemical calculations; Bragg diffraction and diffuse scattering: twins, but different; models of real (as opposed to ideal) crystal structures from diffuse scattering; exploiting unexplored neighbourhoods of crystallography to mathematics, physics and chemistry.

Influence of Nitrogen Substitution on the Electronic Structure of Ti2O3: Insights into the Doping‐Induced Insulator‐to‐Metal Transition

“…In contrast to the experimentally thermal‐induced case, [ 32 ] N substitution in Ti 2 O 3 resulted in a reduction in the c ‐axis parameters in the present study. Nonetheless, the short d ∥ c (2.636 Å at 0 K) in the N‐substituted model is comparable to that in the high‐temperature metallic phase of Ti 2 O 3 (2.670 Å at 565 K [ 32 ] ). This may indicate a situation different from known thermally‐excited results of the crystal structure with an IMT behavior in Ti 2 O 3 .…”

“…Compared with a pure Ti 12 O 18 cell, the d ∥ c in the N‐substituted model reduces from 2.850 to 2.636 Å, whereas d ⊥ c increases marginally from 2.980 to 3.030 Å. In contrast to the experimentally thermal‐induced case, [ 32 ] N substitution in Ti 2 O 3 resulted in a reduction in the c ‐axis parameters in the present study. Nonetheless, the short d ∥ c (2.636 Å at 0 K) in the N‐substituted model is comparable to that in the high‐temperature metallic phase of Ti 2 O 3 (2.670 Å at 565 K [ 32 ] ).…”

“…[ 36,37 ] It shifts to a lower BE (approximately 396 eV) as the TiN film is oxidized, and presumably forms an oxynitride. [ 32 ] This indicates that the N atoms are most likely to be incorporated into the oxide lattice in the form of substitutional N. The weak peak at a higher BE of approximately 400 eV is generally assigned to molecularly surface chemisorbed N. [ 38 ] This implies an NH 3 ‐terminated surface. The incorporation of N into the lattice is corroborated further by the N K ‐edge absorption spectra shown in Figure 2c.…”

“…These include the unit cell lattice constants ( a , b , and c ) and Ti–Ti dimerization distance. For pure Ti 12 O 18 , the lattice parameters a and b are underestimated marginally (by ≈0.91%) and the lattice parameter c is overestimated by ≈5.7%, compared with the experimental data at 296 K. [ 32 ] Substituting O with N in Ti 2 O 3 (i.e., in an N‐substituted cell), the optimized atomic coordination yields the following values of the lattice constants: a = 5.1382 Å, b = 5.1540 Å, and c = 13.998 Å. This corresponds to a slight lattice‐constant mismatch ( a ≠ b ) ≈ 0.3%.…”

Ultrahigh Energy Storage in Tungsten Bronze Dielectric Ceramics Through a Weakly Coupled Relaxor Design

“…h) The measurement schematic to determine the incommensurate superlattice incommensurability parameter δ . [ 51 ]…”