Alice and Joseph in crystal-land
The structure of crystals could not, at the time, be seen directly with a microscope, but had to rely on diffraction. The geometry of the locations of the different diffracted beams/spots allow the structure to be represented in a virtual space which is called "reciprocal space".
Diffraction patterns obtained from a coherent
X-ray diffraction experiment on an
artificial crystal of electronic circuit. © IUCr Journals
Using mathematics to visualise crystals
A precise mathematical relationship, the "Fourier Transform", exists between the "reciprocal space" observed by diffraction and the real structure of the crystal in "direct space".In order to "understand" this relationship, think of Alice (in Wonderland), who has a direct view of the world of the crystal and its atoms, and Joseph (Fourier), who can only see those produced by the diffraction spots!
Diffraction pattern of a
metal powder containing
crystals of various sizes.
Source: G. Artioli
Travelling into "reciprocal space"
The direct observation of "reciprocal space" via diffraction enabled crystallographers to see the symmetry of a crystal, the dimensions of its building block or "unit cell" and finally to "see" the atoms themselves: the diffraction pattern is a fingerprint which identifies each crystal.
Joseph's vision of an object that
is partially disordered, like wood
or the threads of a spider's web
(the spots are diffuse and large).
© IUCr Journals
