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)
 Simple Cubic (SC) (Lattice type P)
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:
\[
\frac{[\text{total number of atoms}][\text{atomic volume}]}{[\text{Unit cell volume}]}
\]