Beauty, Form and Function: An Exploration of SymmetryBeauty, Form and Function: An Exploration of Symmetry

Asset No. 36

Lecture III-9

Laboratory Studies of Crystal Symmetry

PART IIISymmetry in Crystals

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

Preparing Crystals

A synthetic, single crystal rod of an ‘apatite’ containing neodymium and silicon. Apatite is hexagonal P63/m.

A tiny crystal fragment of ‘apatite’ glued to head of a

glass fiber ready for the diffraction experiment.

The X-ray Diffractometer

X-ray detector

X-ray source

crystal

The goniometer that precisely rotates the crystal through 3D

space

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

Symmetry and Crystal Structure DeterminationAn hexagonal apatite X-ray crystal diffraction pattern collected along the [001] projection. This is consistent with P63/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.

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.

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