1. Beauty, Form and Function: An Exploration of Symmetry Asset No. 36 Lecture III-9 Laboratory Studies of Crystal Symmetry PART III Symmetry in Crystals

2. By the end of this lecture, you will be introduced to: the basic principles and methods of collecting X-ray diffraction patterns to determine crystal symmetry scanning electron of small facetted crystals demonstrating that symmetry of hand-held mineral samples can be replicated at micro- and nano-scales Objectives

3. Preparing Crystals A synthetic, single crystal rod of an ‘apatite’ containing neodymium and silicon. Apatite is hexagonal P6 3 /m. A tiny crystal fragment of ‘apatite’ glued to head of a glass fiber ready for the diffraction experiment.

4. The X-ray Diffractometer X-ray detector X-ray source crystal The goniometer that precisely rotates the crystal through 3D space

5. Collecting X-ray Diffraction Patterns The apatite X-ray crystal diffraction patterns collected at different orientations. A close-up of the apatite crystal mounted on a glass fiber

6. Symmetry and Crystal Structure Determination An hexagonal apatite X-ray crystal diffraction pattern collected along the [001] projection. This is consistent with P6 3 /m. Through modelling both the position and intensity of the diffraction spots the crystal structure of the apatite is revealed, including all atom types (Nd, Si, O) and their fractional co-ordinates inside the unit cell.

7. Scanning Electron Microscopy Low magnification showing entire crystal High magnification of one facet of the crystal SEM of ‘hybrid’ perovskites useful as solar electricity collectors.

8.  Large crystals are not suitable for X-ray diffraction as most of the X-rays are absorbed instead of diffracted  Small crystals deliver X-ray diffraction patterns with sharp and intense peaks.  The position of the diffraction spots gives the unit cell size  The intensity of the diffraction spots gives the symmetry  The scanning electron microscope is an ideal tool for studying micro and nano-crystal shape  The principles of symmetry hold at all scales. Summary