Solid State Chemistry Lecture 1: Introduction to Computer Modelling in Solid State Chemistry

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Solid State Chemistry Lecture 1 Introduction to
Computer Modelling in Solid State Chemistry

• Rob Jackson
• School of Chemistry and Physics
• Keele University
• r.a.jackson_at_chem.keele.ac.uk

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Contents of Lecture

• Introduction to computer modelling
• How are interatomic forces represented
• Calculation of the lattice energy of a solid
• Lattice energy minimisation
• Modelling the bulk structure of solids
• examples

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Introduction to Computer Modelling - 1
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Introduction to Computer Modelling - 2

• The aim is to build a computational description
  of a crystal
• Store atom positions (use translational symmetry
  to build up the structure from the unit cell)
• Define interatomic forces between atoms or ions
  using simple functions (discussed next)

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How are interatomic forces represented

• The most important forces responsible for bonding
  in inorganic materials are
• electrostatic (in ionic solids)
• electron repulsion
• van der Waals attractive forces
• Other interactions are important in molecular
  crystals and covalent materials

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Interatomic potentials

• These forces can be represented by simple
  mathematical functions called potential energy
  functions or interatomic potentials.
• For example the Buckingham Potential
• V(r) q1q2/r A exp (-r/) C r-6

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Calculation of the lattice energy of a solid

• The lattice energy is calculated by summing all
  the interactions between atoms or ions
  represented by potentials.
• Ulatt (q1q2/r A exp (-r/) C r-6)
• Note all terms and Ulatt itself depend on r.

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Lattice Energy Minimisation

• The structure adopted by solids has minimum
  lattice energy.
• By varying r and also by varying the unit cell
  sides and angles we can find the structure
  having minimum lattice energy.
• Other properties can then be calculated at the
  minimum energy structure.

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Modelling the bulk structure of solids

• Example topaz (Al2SiO4(OHF)2)
• A mineral with a complex structure which is of
  commercial and technological importance.
• Structure consists of linking SiO4 tetrahedra and
  AlO4(OHF)2 octahedra.
• Natural samples vary mainly in OHF ratio.
• Colour variations are due to presence of metal
  dopants.

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Topaz - Al2SiO4(OHF)2

• A mineral of commercial value as a gemstone
• Technological applications include radiation
  dosimeters

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Developing a Potential Model

• Interatomic potentials were obtained by
  transferral from previous aluminosilicate
  simulations with Al-O and Al-F potentials fitted
  to the F-topaz structure and properties.
• Calculated and experimental lattice parameters
  can be compared

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Experimental and calculated lattice parameters
for F- and OH-topaz
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Other information that may be obtained on topaz

• Phonon frequencies vibrational frequencies of a
  solid material that may be measured using
  infra-red or Raman techniques a good test of
  the computer model.
• How do the structure and properties vary with the
  FOH ratio
• Properties of imperfect topaz

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Modelling defects in solids

• Defects classified as
• Vacancies (missing atoms/ions)
• Interstitials (extra atoms/ions occupying
  non-lattice sites)
• Substitutions
• Procedure is to calculate the energy involved in
  creating the defect and by energy minimisation
  to see how the structure changes.

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Application to topaz

• For example for topaz we could calculate
• The energy of substitution of a different metal
  ion at the Al or Si site which substitute most
  easily
• The preferred substitution site for different
  metal ions in topaz important in understanding
  the properties of the material