Alice and Joseph in crystal-land Josegh Fourier 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". Using mathematics to visualise crystals Travelling into"reciprocal space A precise mathematical relationship,the "Fourier The direct observation of "reciprocal space"via Transform",exists between the "reciprocal space" diffraction enabled crystallographers to see the observed by diffraction and the real structure of the symmetry of a crystal,the dimensions of its crystal in "direct space". building block or"unit cell"and finally to"see"the atoms themselves:the diffraction pattern is a In order to 'understand'this relationship,think of finger print which identifies each crystal. Alice (in Wonderland),who has a direct view of the world of the crystal and its atoms,and that of To understand more... Joseph (Fourier),who can only see those produced by the diffraction spots! Diffraction may appear complicated because it provides an inverse image,but this is nothing more than a superposition of sine waves,discovered by Joseph Fourier when he was the state representative "prefet de Grenoble"under Napoleon the First. *61:0065006806. Gr-jomnal J IYCr2014