By Klaus Hermann

A helpful studying device in addition to a reference, this ebook offers scholars and researchers in floor technology and nanoscience with the theoretical crystallographic foundations, that are essential to comprehend neighborhood constitution and symmetry of bulk crystals, together with excellent and actual unmarried crystal surfaces. the writer offers with the topic at an introductory point, supplying a variety of picture examples to demonstrate the mathematical formalism. The e-book brings jointly and logically connects many likely disparate structural matters and notations used often by means of floor scientists and nanoscientists. quite a few routines of various hassle, starting from easy inquiries to small learn initiatives, are incorporated to stimulate discussions concerning the various subjects.

From the contents:

Bulk Crystals, 3-dimensional Lattices

- Crystal Layers, Two-Dimensional Lattices, Symmetry

- excellent unmarried Crystal Surfaces

- actual Crystal Surfaces

- Adsorbate layers

- Interference Lattices

- Chiral Surfaces

- Experimental research of actual Crystal Surfaces

- Nanoparticles and Crystallites

- Quasicrystals

- Nanotubes

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**Example text**

The dashed lines are meant to assist the visual orientation inside the ﬁgures. 22 Shape of Wigner–Seitz √ cells of the centered tetragonal (ct) lattice for diﬀerent ratios q = c/a. Here q = 1 and q = 2 represent the bcc and fcc lattice, respectively. The top ﬁgures refer to rectangular blocks of a ﬁctitious monoatomic ct crystal illustrating the lattice structure for corresponding ratios q. The ratio q = c/a of the two lattice constants determines the actual lattice type, √ where q = 1 reﬂects the bcc and q = 2 yields the fcc lattice.

21 compare morphological unit cells (Niggli cells) with WSCs for the bcc- and fcc lattices. Both polygonal WSCs are highly symmetric, which reﬂects the large number of point symmetry elements of the cubic lattice. This applies also to the WSC of the sc lattice which forms a cube and is identical in shape with the morphological unit cell. A complete set of WSCs for all 14 Bravais lattices can be found in [32, 50]. 20 (a) Morphological unit cell (Niggli cell) and (b) Wigner–Seitz cell of the bcc lattice.

It also includes the corresponding names for mirror symmetry planes and inversion centers. The four diﬀerent rotation axes can distinguish between the diﬀerent types of three-dimensional lattices. First, there are lattices that do not possess any rotational axis. They form the most general type of Bravais lattices and will be called triclinic-P. 3 will lead to another triclinic-P lattice, that is, will not create any new lattice type. 23, is the only member of the triclinic crystal system. 23 Morphological unit cell of the triclinic-P lattice with lattice vectors R 1 , R 2 , R 3 and angles α, β, γ labeled accordingly.