Periodicity of lattices

The results of calculations allow supposing the existence of polymerized FCC crystal phase of C28 with period of the lattice a = 13.080 A (the space symmetry group coincides with symmetry group of crystal NaCl and period of lattice is twice more than distances between the centers of neighboring molecules). One can expect the solid phase of C28 is insulator with forbidden gap width about 2 eV. The results of our calculations don t contradict to the data of earlier theoretical searches [12-13],... 

Each of these is confined to a site or point, thus, they are called point defects. There are more disl(x ations disturbing the periodicity of lattice sites grain boundaries and surfaces spatially confining the crystal which would have to be infinite if ideal voids and inclusions that are three-dimensional aggregates of point defects of a kind. Depending on their geometries, they are often called line defects, planar defects and volume defects, respectively. 

Tq and Uo are close to the natural period of lattice oscillations and interatomic binding energy (or cohesive energy). The constant 3 is a measure of the effectiveness of the stress in overcoming the bond activation barrier Uq. 

Periods of lattices a, b, c together with angles a, y, plane indexes (/ , k, 1) and interplanar spacing d are bound by a so-called quadratic form. For the simplest case of a cubic crystal, the quadratic form is presented by the equation... 

In LEED experunents, the matrix M is detennined by visual inspection of the diffraction pattern, thereby defining the periodicity of the surface structure the relationship between surface lattice and diffraction pattern will be described in more detail in the next section. 

One now wonders whether these two phenomena are to be observed also for the whole two-dimensional surface of a crystal non-locking of the crystal surface in spite of lattice periodicity, and divergence of the fluctuation-induced thickening of the interface (or crystal surface), and in consequence the absence of facets. The last seems to contradict experience crystals almost by definition have their charm simply due to the beautifully shining facets which has made them jewelry objects since ancient times. 

It turns out that, in the CML, the local temporal period-doubling yields spatial domain structures consisting of phase coherent sites. By domains, we mean physical regions of the lattice in which the sites are correlated both spatially and temporally. This correlation may consist either of an exact translation symmetry in which the values of all sites are equal or possibly some combined period-2 space and time symmetry. These coherent domains are separated by domain walls, or kinks, that are produced at sites whose initial amplitudes are close to unstable fixed points of = a, for some period-rr. Generally speaking, as the period of the local map... 

Gamer and Jennings [431] studied nucleation during the dehydration of potassium and ammonium chromium alums. Detailed kinetic measurements were made for the relatively enhanced rate of nucleation which followed admission of water vapour to the solid after a period of vacuum nucleation. This catalytic effect of water vapour is ascribed to its participation in the reorganization of the lattice which had collapsed during previous treatment in vacuum. 

A Bloch function for a crystal has two characteristics. It is labeled by a wave vector k in the first Brillouin zone, and it can be written as a product of a plane wave with that particular wave vector and a function with the "little" period of the direct lattice. Its counterpart in momentum space vanishes except when the argument p equals k plus a reciprocal lattice vector. For quasicrystals and incommensurately modulated crystals the reciprocal lattice is in a certain sense replaced by the D-dimensional lattice L spanned by the vectors It is conceivable that what corresponds to Bloch functions in momentum space will be non vanishing only when the momentum p equals k plus a vector of the lattice L. 

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