Structures of Simple Inorganic Solids

- a Lecture for the Oxford University / Sutton Trust Summer School 1999

Dr S.J. Heyes - Dept. Chemistry, University of Oxford

Why Study Solids?

1. ALL Compounds are Solids under suitable conditions of temperature and pressure. Many exist only as solids.

2. Solids are of immense Technological Importance

Appearance

Precious and Semi-precious Gemstones of many varieties

Mechanical Properties

Metals/Alloys, e.g. Titanium for aircraft
Cement/Concrete Ca₃SiO₅
'Ceramics', e.g. clays, BN, SiC
Lubricants, e.g. Graphite, MoS₂
Abrasives, e.g. Diamond,
- Quartz (SiO₂),
  Corundum

Electrical Properties

Metallic Conductors, e.g. Cu, Ag...
Semiconductors, e.g. Si, GaAs
Superconductors, e.g. Nb₃Sn, YBa₂Cu₃O₇
Electrolytes, e.g. LiI in pacemaker batteries
Piezoelectrics, e.g. a Quartz (SiO₂) in watches

Magnetic Properties

e.g. CrO₂, Fe₃O₄ for recording technology

Optical Properties

Pigments, e.g. TiO₂ in paints
Phosphors, e.g. Eu³⁺ in Y₂O₃ is red on TV
Lasers, e.g. Cr³⁺ in Al₂O₃ is ruby
Frequency-doubling of light, e.g. LiNbO₃

Catalysts

Zeolite ZSM-5 (an aluminosilicate)
- - Petroleum refining
- - methanol octane

Sensors

Oxygen sensor, e.g. ZrO₂/CaO solid solution

3. Solids (especially Crystals) have always been fascinating

Some Historical Landmark Events

Antiquity Gemstones (especially diamond, sapphire, emerald & ruby) are much prized. Indeed some still attribute magical properties, such as healing to crystals!
64 BC Strabo names Quartz krystlloz (crystallum in Latin), hence our 'crystal'
1611 Kepler, after making observations with the newly invented microscope suggests that the hexagonal symmetry of snowflakes is due to "regular packing of the constituent particles"
1913 W.H. & W.L. Bragg use orientation dependence of X-ray diffraction from a single crystal to solve the structure of NaCl (& subsequently diamond etc...)
1926 Goldschmidt's spherical atom formulation of structures
1957 Müller first visualizes individual atoms in metals using Field-Ion Microsopy
today >200,000 Crystal structures (internal atom coordinates) stored in databases

Some Basic Definitions

LATTICE = An infinite array of points in space, in which each point has identical surroundings to all others.

CRYSTAL STRUCTURE = The periodic arrangement of atoms in the crystal.

It can be described by associating with each lattice point a group of atoms called the MOTIF (BASIS)

UNIT CELL = The smallest component of the crystal, which when stacked together with pure translational repetition reproduces the whole crystal

2D LATTICES

e.g. the fused hexagonal pattern of a single layer of GRAPHITE

Analysing a 3D solid

e.g. Graphite = a staggered arrangement of stacked hexagonal layers

Structures of Metallic Elements

but which structure makes the best use of space?

1926 Goldschmidt proposed atoms could be considered as packing in solids as hard spheres

This reduces the problem of examining the packing of like atoms to that of examining the most efficient packing of any spherical object - e.g. have you noticed how oranges are most effectively packed in displays at your local shop?

CLOSE-PACKING OF SPHERES

A single layer of spheres is closest-packed with a HEXAGONAL coordination of each sphere

A second layer of spheres is placed in the indentations left by the first layer

space is trapped between the layers that is not filled by the spheres
TWO different types of HOLES (so-called INTERSTITIAL sites) are left
- OCTAHEDRAL (O) holes with 6 nearest sphere neighbours
- TETRAHEDRAL (T±) holes with 4 nearest sphere neighbours

When a third layer of spheres is placed in the indentations of the second layer there are TWO choices

The third layer lies in indentations directly in line (eclipsed) with the 1st layer
- Layer ordering may be described as ABA
The third layer lies in the alternative indentations leaving it staggered with respect to both previous layers
- Layer ordering may be described as ABC

Close-Packed Structures

The most efficient way to fill space with spheres?

Kepler proposed this in 1611, in August 1998 Prof. Thomas Hales of the University of Michigan announced a computer-based solution. This proof is contained in over 250 manuscript pages and relies on over 3 gigabytes of computer files and so it will be some time before it has been checked rigorously by the scientific community to ensure that the Kepler Conjecture is indeed proven!

Other materials can be considered to form in similar structures to metals

Structures of Compounds?

Consider the holes in a packed-sphere structure to be filled by spheres of another type

NaCl Rock Salt (Halite)

Counting Atoms in 3D Cells

Atoms in different positions in a cell are shared by differing numbers of unit cells

Vertex atom shared by 8 cells Þ ¹/₈ atom per cell
Edge atom shared by 4 cells Þ ¹/₄ atom per cell
Face atom shared by 2 cells Þ ¹/₂ atom per cell
Body unique to 1 cell Þ 1 atom per cell

Two Forms of Zinc Sulfide, ZnS

but how do they differ?

Structures with the Diamond FRAMEWORK

YBa₂Cu₃O₇ - the 1:2:3 Superconductor

the first material to superconduct at >l-N₂ temperature

Information about Superconductors is available from the Chemistry IT Centre's Virtual Laboratory

Silicate Minerals - Networks of Tetrahedral SiO₄^4- Units

Samples of minerals can be found in the Collections of the University Museum at Oxford

Zeolite ZSM-5

ZSM-5 is considered in the Molecule of the Month feature

A couple of fun things to do on the web!

"Escher Web Sketch" by Wes Hardaker and Gervais Chapuis

A really fun way to create your own 2D patterns with different lattice symmetries is the

Crystal Structures by Prof. Winston Chan, University of Iowa

Prof. Chan has written Java applets to allow you to view and manipulate crystal structures within your web browser. These are less versatile than viewing in the CrystalMaker program, but have the distinct advantage of being computer-platform independent - so a good complement to this site if you are using a PC.

Now on to the Practical, Structures of Solids!