Analytical description of nanowires III: regular cross sections for wurtzite structures

König, D.; Smith, S.C.

doi:10.1107/S2052520622004954

Figure 12
Geometric relations for the wurtzite lattice structure along the c = [0001] growth vector. The unit cell in the {0001} plane is shown in yellow and its relevant lattice vectors a₁, a₂ and a₃ are shown in blue. The unit area $[A_{\hexagon}]$ (grey–green) for the {0001} plane is defined by the area of a six-membered ring, consisting of six equilateral triangles $[A_{\Delta}]$ = $[{1 \over 6}\,A_{\hexagon}]$ (red). The distance increments required for calculating the lengths of the {1000} and $[\{1\bar{1}00\}]$ interfaces are shown by $[s_{\rm IF,1\bar{1}00}]$ and $[s_{\rm IF,1000}]$ , respectively, with local atomic bonds shown. As an auxiliary parameter, we show the height $[h_{\Delta}]$ and its relevant fractions of the congruent equilateral triangles. All length parameters other than the lattice vectors are shown in purple. Grey lines show the $[\{1\bar{1}00\}]$ interfaces, which require some additional derivations in terms of fractional $[h_{\Delta}]$ and a fractional area $[A_{\triangleright}]$ = $[{1 \over 3}\,A_{\Delta}]$ . A scheme of relevant lattice vectors within the {0001} plane is shown on the upper left, with c being orthogonal to the {0001} plane; indices shown in grey present alternative combinations of lattice vectors.

STRUCTURAL SCIENCE
CRYSTAL ENGINEERING
MATERIALS

ISSN: 2052-5206

Volume 78| Part 4| August 2022| Pages 665-677

https://doi.org/10.1107/S2052520622004954

Open

access

Search IUCr Journals		doi		Advanced search
Author		volume	page