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PX3012 The Solid State Course coordinator: Dr. J. Skakle CM3020 Solid State Chemistry Course coordinator: Dr. J. Feldmann

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SOLID STATE Crystals Crystal structure basics unit cells symmetry lattices Some important crystal structures and properties close packed structures octahedral and tetrahedral holes basic structures ferroelectricity Diffraction how and why - derivation

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Objectives By the end of this section you should: be able to identify a unit cell in a symmetrical pattern know that there are 7 possible unit cell shapes be able to define cubic, tetragonal, orthorhombic and hexagonal unit cell shapes

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Why Solids? most elements solid at room temperature atoms in ~fixed position simple case - crystalline solid Crystal Structure Why study crystal structures? description of solid comparison with other similar materials - classification correlation with physical properties

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Crystals are everywhere!

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More crystals

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Early ideas Crystals are solid - but solids are not necessarily crystalline Crystals have symmetry (Kepler) and long range order Spheres and small shapes can be packed to produces regular shapes (Hooke, Hauy) ?

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Group discussion Kepler wondered why snowflakes have 6 corners, never 5 or 7. By considering the packing of polygons in 2 dimensions, demonstrate why pentagons and heptagons shouldnt occur.

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Definitions 1. The unit cell The smallest repeat unit of a crystal structure, in 3D, which shows the full symmetry of the structure The unit cell is a box with: 3 sides - a, b, c 3 angles -,,

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Seven unit cell shapes Cubica=b=c = = =90° Tetragonala=b c = = =90° Orthorhombica b c = = =90° Monoclinica b c = =90°, 90° Triclinica b c 90° Hexagonala=b c = =90°, =120° Rhombohedrala=b=c = = 90° Think about the shapes that these define - look at the models provided.

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2D example - rocksalt (sodium chloride, NaCl) We define lattice points ; these are points with identical environments

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Choice of origin is arbitrary - lattice points need not be atoms - but unit cell size should always be the same.

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This is also a unit cell - it doesnt matter if you start from Na or Cl

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- or if you dont start from an atom

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This is NOT a unit cell even though they are all the same - empty space is not allowed!

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In 2D, this IS a unit cell In 3D, it is NOT

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All M.C. Escher works (c) Cordon Art-Baarn-the Netherlands. All rights reserved.

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Examples The sheets at the end of handout 1 show examples of periodic patterns. On each, mark on a unit cell. [remembering that there are a number of different (correct) answers!]

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Summary Unit cells must link up - cannot have gaps between adjacent cells All unit cells must be identical Unit cells must show the full symmetry of the structure next section

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