= Crystal structure
{tag=Solid}
{wiki}
A <crystal structure> specifies the <chemical species> and spatial arrangement of the <chemical atoms> or <ions> in a crystal. For an ideal periodic structure, separate two ingredients: a <Bravais lattice> specifies the <translations> that repeat the arrangement, and an <atomic basis of a crystal> specifies the chemical motif repeated at every <lattice point>. The outward shape, or <crystal habit>, is a different description: the internal arrangement is what this article describes.
For a concrete two-dimensional model, choose <primitive lattice translation vectors> $a_1=(2,0)$ and $a_2=(0,1.5)$ in arbitrary length units. At every <lattice point> $R=ma_1+na_2$, with <integers> $m,n$, place species A at $R$ and a different species B at $R+(0.65,0.55)$. Translating by $a_1$ or $a_2$ preserves both the positions and their chemical labels. Translating by $(0.65,0.55)$ sends one A position to a B position, so it is not a <translation symmetry> of the labeled structure. A picture of dots with the labels erased can therefore conceal essential chemical information.
\Image[/crystal-translations-and-two-site-motif.png]
{title=A translation lattice decorated with a two-site chemical motif}
{id=image-crystal-translations-and-two-site-motif}
{description=Original two-dimensional model: the same two-site <atomic basis of a crystal> is repeated at every <lattice point>. Each shaded <primitive unit cell> has <area> $2(1.5)=3$ and contains one A site and one B site; shifting the cell boundary avoids shared boundary sites. Dots are positions, not atomic radii, and the two-site motif need not be a <molecule>.}
A <primitive unit cell> contains one <lattice point>, but may contain several <chemical atoms>. A conventional <unit cell> can contain several <lattice points> to display the <symmetry> more clearly. Thus the conventional cube of a <face-centered cubic lattice> contains four <lattice points>, whereas a <body-centered cubic lattice> has two. Neither lattice name alone specifies which <chemical species> occupies the repeated motif. The <NaCl conventional cell and coordination> example makes the distinction explicit.
This separation is useful experimentally: <interplanar spacings> constrain the repeating geometry, while relative <wave intensities> also depend on the <atomic basis of a crystal> through the <crystal basis structure factor>. The <Bragg crystal reflection experiment of 1913> describes the <X-ray> spectrometer, angular scans and detector checks in detail. Its conversion from angle to length is developed under <Bragg's law>; a geometrically possible reflection can still have zero <wave intensity>.
<William Lawrence Bragg>'s 1913 structure determination supplied a complementary test. He directed <X-rays> through <sodium chloride> sections cut parallel to a cube face and recorded spots on photographic plates. Comparing section thicknesses tested how transmission altered the pattern: the relative spot strengths changed. Comparing related <salts> led him to two interpenetrating <face-centered cubic lattices>, one for each kind of constituent. He explicitly distinguished evidence for that arrangement from the still-needed identification of a single <chemical atom> with each scattering center. The photographs were evidence for a structural model, not direct pictures of labeled <ions>.<The Structure of Some Crystals as Indicated by their Diffraction of X-rays by William Lawrence Bragg>[W. L. Bragg (1913), pp. 262–263, Figs. 8–9 and Tables VII–IX: oriented NaCl sections and thickness comparison; pp. 264–265, Fig. 10: two arrays and the remaining atomic-assignment question]{ref}
Back to article page
