Lattice angles

Our discussion of electronic structure has been in terms of band filling only. Of course, there is a lot more to know about band structures. The density of states represents only a highly simplified representation of the actual electronic structure, which ignores the three-dimensional structure of electron states in the crystal lattice. Angle-dependent photoemission gives information on this property of the electrons. The interested reader is referred to standard books on solid state physics [9,10] and photoemission [16,17]. The interpretation of photoemission and X-ray absorption spectra of catalysis-oriented questions, however, is usually done in terms of the electron density of states only. 

Crystalline surfaces can be divided into five Bravais lattices (Fig. 8.3) according to their symmetry. They are characterized by the lattice angle a and the lengths of the lattice vectors ai and a2. The position vectors of all individual surface atoms can be indicated by... 

Cell parameters. In Table 6 we report atmospheric pressure lattice parameters and unit cell volumes for / -, a- and 5 -HMX as obtained from MD simulations at 295 K. Also shown for comparison are the experimental results at the same temperature. It can be seen that the simulation results are in good agreement with experiment. The largest percent error in unit cell volume, 1.4%, occurs for a-HMX. The lattice angles are essentially exact with the exception of / -HMX, for which the monoclinic angle / is 3.6% too small. This error is compensated by errors of -4.7% and 3.7% in lattice lengths b and c,... 

A standard set of reference axes and equations to describe spontaneous strains is now well established (Schlenker et al. 1978, Redfern and Salje 1987, Carpenter et al. 1998a). The orthogonal reference axes, X, Y and Z, are selected so that Y is parallel to the crystallographic y-axis, Z is parallel to the normal to the (001) plane (i.e. parallel to c ) and X is perpendicular to both. The +X direction is chosen to conform to a right-handed coordinate system. Strain is a second rank tensor three linear components, cn, 622 and 33 are tensile strain parallel to X, Y and Z respectively and co, 623, eu are shear strains in the XZ, YZ and XY planes, respectively. The general equations of Schlenker et al. (1978) define the strains in terms of the lattice parameters of a crystal (a, b, c, a, P, y, where P is the reciprocal lattice angle) with respect to the reference state for the crystal ( , bo, Co, cto, Po,Yo) ... 

Polymorphism is defined as the occurrence of different crystal modifications of the same molecule or polymer possessing the same monomeric unit. The various modifications are characterized by different lattice constants or lattice angles, and, consequently, different unit cells. The different unit cells result in microscopically perceptible differences in crystal shape, solubility, melting point, etc. 

Angle between the director n and the main axis of a molecule i Lattice angles Azimuth angle... 

Note for rhe >mbohedral lattices., angle 0, the hkl) spacings scale as ... 

Lattice angle Space group Pa3 P6 /mmc PA2/mnm R3m Cmca R3m Pm3m PS Immc 86.0 deg... 

---