# Solid Metals¶

• Form a crystalline lattice structure
• Form using metallic bonds - electron delocalisation within the lattice matrix

## Solid state physics and materials science¶

• We need to understand structural chemistry as the structure of molecules determines its function
• We can characterise solids using various methods
• XRPS/XRD
• Electron microscopy
• Thermal analysis
• Spectroscopy
• Conductivity characterisation
• Etc..
• In understanding the properties we can tune them, such as:
• Magnetism
• Conductivity
• Sorption
• Luminescence
• Defects - point, dislocation, grain boundaries
• Doping to produce strategic defects
• We can also synthesise such products using:
• Hydrothermal synthesis, soft chemistry and physical manipulation of the environment

## Categories of solids¶

• Crystalline solids are periodic systems, consisting of a unit cell, repeated over and over
• They pack in a continuous pattern, occasionally with defects
• Amorphous solids have little, if any long range order
• Polycrystalline Solids are an aggregate of smaller crystalline grains, or fragments that pack together in a random fashion

## Atoms as spheres¶

• Atoms can be simplified to be treated as spheres, for purposes of packing efficiency and bonding properties
• The definition of the bond length is based on the type of bond it forms
• The general form is that the radius is half the bond length between two atoms of the same type

## Structure¶

Lattice

• Is the mathematical descriptor of the symmetry of the components of the un it cell
• E.g. Simple cubic, body centred cubic, face centred cubic

Motif

• Is the specific atoms/molecules that are placed on each of the points as defined by the lattice

Unit Cell

• Is the 3D translational structure (the grid) that forms the overall periodic structure
• How to move the components of the cell to make the overall lattice (translational vectors)

Coordination number

• Is the amount of atoms that any atom is coordinated with
• How many atoms are there to coordinate a stable structure
• Can be defined as “the number of nearest neighbours”

Structures of unit cells

• These are defined by the equivalence of angles and lengths
Crystal System Restriction Axis Restriction Angles
Triclinic - -
Monoclinic - $$\alpha=\gamma=90^\circ$$
Orthorhombic - $$\alpha=\beta=\gamma=90^\circ$$
Tetragonal $$a=b$$ $$\alpha=\beta=\gamma=90^\circ$$
Trigonal $$a=b$$ $$\alpha=\beta=90^\circ,\:\gamma=120^\circ$$
Hexagonal $$a=b$$ $$\alpha=\beta=90^\circ,\:\gamma=120^\circ$$
Cubic $$a=b=c$$ $$\alpha=\beta=\gamma=90^\circ$$

## Structure of metals¶

• In this unit we’ll only really cover the structure of metals, within a cubic system
• Metal crystals are simple since they don’t deform too much, so a spherical approximation can be made
• All of them crystallise into one of four basic structures

• Simple Cubic (SC) (Lattice type P)
• $$52\%$$ packing efficiency
• Contains one atom $$8\frac{1}{8}$$
• Coordination number of $$6$$
• Body Centred Cubic (BCC) (Lattice type I)
• $$68\%$$ packing efficiency
• Contains two atoms $$\big(8\frac{1}{8}\big)+1$$
• Example elements (STP) - Li, Na, K, Ba, Rb, V, Cr, Fe
• Coordination number $$8$$
• Cubic Closest Packed (CCP) or Face Centred Cubic (FCC) (Lattice type F)
• $$74\%$$ packing efficiency
• Contains $$4$$ atoms $$\big(8\frac{1}{8}\big)+\big(6\frac{1}{2}\big)$$
• Example elements - Al, Cu, Au, Ir, Pb, Ni, Pt, Ag
• Coordination number $$12$$
• Hexagonal Closest Packed (HCP)

## Packing Efficiency¶

• This is a metric of how much space is left between the atoms when packing them together
• They are simple to calculate, given a single parameter, utilising Pythagoras’ theorem
• The basic formula is:
$\frac{[\text{total number of atoms}][\text{atomic volume}]}{[\text{Unit cell volume}]}$