Chemistry · Ch 6 — Solid State
Two Dimensional Close Packing
Two Dimensional Close Packing
A two-dimensional planar layer can be built from one-dimensional rows in exactly two distinct ways:
- AAA... type. The one-dimensional row is repeated in the second dimension so that every row aligns exactly with the row before it -- all spheres of every row line up vertically as well as horizontally. Because every row is identical to (and directly above) the first, this is called the AAA type arrangement. In this layer, each sphere touches 4 neighbours: two in its own row, and one each in the row above and the row below.
- ABAB... type. Here the spheres of the second row are shifted sideways to nestle into the depressions (gaps) left between the spheres of the first row -- this second, offset row is called the B-type row. The third row repeats the first row's A-type position, the fourth repeats the second row's B-type position, and so the pattern ABAB... continues indefinitely. In this arrangement, each sphere is in contact with 6 neighbouring spheres rather than 4. …
What this figure shows. A rectangular grid of green spheres arranged in perfectly aligned rows and columns, every sphere sitting directly above the sphere in the row below and directly beside the sphere in the same column -- each interior sphere touches exactly 4 neighbours (two in its own row, one above, one below). Every row here repeats the exact same one-dimensional pattern of Section 6.6.1 without any sideways shift, which is why the whole layer is labelled the 'AAA...' type -- all rows are identical copies of the first, 'A', row, stacked directly on top of one a …
What this figure shows. A grid of spheres in which the lower rows are green (A-type rows) and one row is pink (the second, B-type row), with the pink row's spheres nested into the depressions between adjacent green-row spheres rather than sitting directly below them; a small diamond outline marks one such depression pocket where a B-row sphere sits -- each sphere in this closer arrangement touches 6 neighbours. Because the second row's spheres sink into the gaps of the first row instead of stacking directly on top of them, the rows sit noticeably closer together (vertically) than in the AAA arrangement -- and it is exactly this ABAB pattern, not AAA, that the text goes on to build the …