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Solid State Background
Published in P.J. Gellings, H.J.M. Bouwmeester, Electrochemistry, 2019
Isaac Abrahams, Peter G. Bruce
The positions of atoms in a crystal can be described with respect to the unit cell using fractional coordinates. Consider a point P located within a unit cell (Figure 3.10). To reach P one has to travel a distance X along a, Y along b, and Z along c. Thus, position P may be described by three fractional coordinates x, y, z, where: x=X/a(X=distancealonga-axis)y=Y/a(Y=distancealongb-axis)z=Z/a(Z=distancealongc-axis)
An Introduction to Crystal Structures
Published in Elaine A. Moore, Lesley E. Smart, Solid State Chemistry, 2020
Elaine A. Moore, Lesley E. Smart
The position of an atom or an ion in a unit cell is described by its fractional coordinates; these are simply the coordinates based on the unit cell axes (known as the crystallographic axes) and are expressed as fractions of the unit cell lengths. It has the simplicity of a universal system that enables unit cell positions to be compared from one structure to another regardless of a variation in the unit cell size.
Basic Principles in Crystallization
Published in Gerard F. Arkenbout, Melt Crystallization Technology, 2021
The diffraction pattern of X-rays may provide a substantial amount of information on the internal structure of a crystal like: details of the unit cell—Analysis of the diffraction pattern will provide information on the dimensions of the unit cell (a, b, c) and the angles between the unit cell sides (α, β, γ).molecular information—Information on the coordinates of the atoms in a molecule can be obtained. These fractional coordinates (x, y, z) are relative to the unit cell dimensions and represent the relative positions of the atoms. These data can be used when aiming at the calculation of bond distances and bond angles.symmetry information—Analysis of the diffraction pattern will also provide information on the number of molecules in a unit cell and the relationship between one molecule and the other molecules, if any, in the unit cell. A combination of these three items of information may result in a characterization of the crystal structure according to one of the 230 so-called space groups using a distinct set of symmetry operators. The space group symbols used show first the lattice type, then the nature of the axes (rotation, inversion, screw). Diad inversion axes correspond either to mirror planes or to glide planes. Other types of rotation, inversion, and screw axes may be indicated. For further information, please refer to International Tables for X-ray Crystallography; Vol. 1 Symmetry Groups, edited by N. F. M. Henry and K. Lonsdale (1969). The technique of X-rays diffraction has appeared to be very successful over the past twenty-five years. A specific computer data base has been set up for organic compounds: the Cambridge Structural Data Base with more than 70,000 entries (Kennard, 1988). Table 2.2 shows the space groups of a number of organic compounds.
The nature of the intermediate phase in K3Na(SeO4)2 crystals: three possible transition paths of the trigonal-monoclinic phase transition
Published in Phase Transitions, 2018
Yu. E. Kitaev, E. M. Roginskii, V. S. Zhandun
The atomic positions are given in fractional coordinates. For atoms occupying the Wyckoff positions (WP) 2d, two coordinates are fixed by symmetry and only one component z (along the c axis) is free. For atoms in the WP 6i, one coordinate is fixed while two others x, z (along the a (b) and c axes) are relaxed. For atoms in 1b (K2) and 1a (Na) positions, all coordinates are fixed by symmetry.