Related Experiment Video
Updated: Oct 1, 2026

X-ray Powder Diffraction in Conservation Science: Towards Routine Crystal Structure Determination of Corrosion Products on Heritage Art Objects
Published on: June 8, 2016
Ab initio determination of a crystal structure by means of the Schrödinger equation
K Bethanis1, P Tzamalis, A Hountas
1Physics Laboratory, Agricultural University of Athens, 75 Iera Odos, Votanikos, Athens 118-55, Greece.
Abstract:
It is shown that the use of the Schrödinger equation may lead to the ab initio determination of the positions of the nuclei in a crystal, given a limited number of diffracted-beam intensities. In particular, it is shown that an extremely simplified Schrödinger equation in physical momentum space provides a sufficiently sound theoretical basis to develop an algorithm using diffraction data alone. This algorithm has been tested with a known 41 atom crystalline structure (not including hydrogen atoms) in space group P1. The extracted information is sufficient to determine the positions of all atoms. In addition, theoretical developments relevant to the connection between momentum space in quantum mechanics and diffraction theory have been formulated.
Related Concept Videos
Determination of Crystal Structures
X-ray Crystallography
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
The Quantum-Mechanical Model of an Atom
Crystal Field Theory - Octahedral Complexes
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Crystal Field Theory - Tetrahedral and Square Planar Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Structures of Solids

