Lattice crystallography

Dislocation, lattice (crystallography) A line of displacement of atoms in a lattice. Often formed during mechanical stress to relieve some of the stress. 

Vacancy, lattice (crystallography) A missing atom at a lattice site. 

These include rotation axes of orders two, tliree, four and six and mirror planes. They also include screM/ axes, in which a rotation operation is combined witii a translation parallel to the rotation axis in such a way that repeated application becomes a translation of the lattice, and glide planes, where a mirror reflection is combined with a translation parallel to the plane of half of a lattice translation. Each space group has a general position in which the tln-ee position coordinates, x, y and z, are independent, and most also have special positions, in which one or more coordinates are either fixed or constrained to be linear fimctions of other coordinates. The properties of the space groups are tabulated in the International Tables for Crystallography vol A [21]. 

Single-crystal surfaces are characterized by a set of Miller indices that indicate tlie particular crystallographic orientation of the surface plane relative to the bulk lattice [5]. Thus, surfaces are labelled in the same way that atomic planes are labelled in bulk x-ray crystallography. For example, a Ni (111) surface has a surface plane... 

Watson G W, P Tschaufeser, A Wall, R A Jackson and S C Parker 1997. Lattice Energy and Free Energy Minimisation Techniques. Computer Modelling in Inorganic Crystallography. San Diego, Academic Press, pp. 55-81. 

X-ray crystallography of potassium, rubidium, and cesium methyls shows completely ionic crystal lattices Weiss, E. Sauermann, G. Chem. Ben, 1970, 103, 265 Weiss, E. Koster, H. Chem. Ber., 1977, 110, 717. 

A special notation is used to describe surface reconstructions and surface overlayers and is described in books on surface crystallography (Clarke, 1985). The lattice vectors a and b of an overlayer are described in terms of the substrate lattice vectors a and b. If the lengths la I = mlal and Ib l = nibl, the overlayer is described as mXn. Thus, a commensurate layer in register with the underlying atoms is described as 1 X 1. The notation gives the dimension of the two-dimensional unit cell in terms of the dimensions of an ideally truncated surface unit cell. 

Palladium hydride is a unique model system for fundamental studies of electrochemical intercalation. It is precisely in work on cold fusion that a balanced materials science approach based on the concepts of crystal chemistry, crystallography, and solid-state chemistry was developed in order to characterize the intercalation products. Very striking examples were obtained in attempts to understand the nature of the sporadic manifestations of nuclear reactions, true or imaginary. In the case of palladium, the elfects of intercalation on the state of grain boundaries, the orientation of the crystals, reversible and irreversible deformations of the lattice, and the like have been demonstrated. 

These are two important special cases. The power and simplicity of diffraction pattern analysis (crystallography) for the analysis of regular structure is a result of Eq. (2.27) and Eq. (2.25). No information is lost if infinite abstract lattices are subjected to Fourier transformation. 

Distortions of the First Kind and Thermal Disorder. In crystallography the best-known example for a lattice distortion of the first kind is the reduction of peak intensity from random temperature movement of the atoms. In materials science a frozen-in thermal disorder of nanostructures25 is observed as well. The result of this kind of disorder is a multiplicative26 attenuation of the scattering intensity by the Debye-Waller factor... 

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