Bart Kahr - Why are Crystals Straight?

Presentation by Prof. Bart Kahr, from the Molecular Design Institute at New York University (NYU).

Abstract: In chemistry, we know the vast majority of what we know about molecular structure from the scattering of X-rays from crystals. Diffraction works so well because crystals have long range translational symmetry. In fact, crystals are straight, by definition. Their sharp edges and flat faces, so unlike most everything else in Nature, “flash forth their symmetry”, according to Federov. Translational symmetry is first and foremost. However, we have shown in the past decade that a large fraction of simple molecular (organic) crystals can be made to grow on the microscale with helicoidal morphologies, as structures with curvature that are decidedly not straight. This is an extraordinarily common fact about crystal form that is very easy to observe. Nevertheless, the forces involved in twisting crystals are difficult to identify. Studies of the mechanisms that give rise to these apparent distortions in crystals that twist as they grow has developed into a meditation and a program of computation aimed at understanding why and when crystals develop translational symmetry. Simulations of nanoscale structures built from crystallographic coordinates for many substances show that when small, crystals are not semi-infinite and they forgo translational symmetry. We have come to see translational symmetry not as a requirement of crystallinity, but rather as an imperfect compromise between free energy and size. Bridging the chasm between the nanoscale and the microscale remains our challenge.