The ability of core-shell nanowires to overcome existing limitations of heterostructures is one of the key ingredients for the design of next generation devices. This requires a detailed understanding of the mechanism for strain relaxation in these systems in order to eliminate strain-induced defect formation and thus to boost important electronic properties such as carrier mobility. Here we demonstrate how the hole mobility of [110]-oriented Ge-Si core-shell nanowires can be substantially enhanced thanks to the realization of large band offset and coherent strain in the system, reaching values as high as 4200 cm²/(Vs) at 4 K and 1600 cm²/(Vs) at room temperature for high hole densities of 10¹⁹ cm^-3. We present a direct correlation of (i) mobility, (ii) crystal direction, (iii) diameter, and (iv) coherent strain, all of which are extracted in our work for individual nanowires. Our results imply [110]-oriented Ge-Si core-shell nanowires as a promising candidate for future electronic and quantum transport devices.

A survey is given of new types of crystallographic faces and forms occurring on modulated crystals which have to be indexed with four integers (hklm). These faces have so far been found on modulated crystals with an average jS-K2S04 structure which can be grown from an aqueous solution and the mineral crystal calaverite (AuTe2) which can be grown from the melt. Interesting data on crystal growth obtained from in situ observations are presented. Among others, spiral-like patterns can be recognized. The occurrence on quasicrystals of crystal forms to be indexed with six integers (hklmno) is discussed and it is shown that these faces can in principle be explained by a generalization of the Hartman- Perdok theory. Crystal forms (hklm) and (hklmno) occurring on modulated and quasicrystals respectively can be explained by the higher than three-dimensional crystallography of de Wolff, Janner and Janssen where these crystals are considered as threedimensional cuts out of a higher than three-dimensional truly translational invariant structure.