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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

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  • 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”

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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

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  • 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:
\[ \frac{[\text{total number of atoms}][\text{atomic volume}]}{[\text{Unit cell volume}]} \]