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PX3012 The Solid State CM3020 Solid State Chemistry Course coordinator: Dr. J. Skakle Course coordinator: Dr. J. Feldmann SOLID STATE Crystals Crystal structure basics unit cells symmetry lattices Diffraction how and why - derivation Some important crystal structures and properties close packed structures octahedral and tetrahedral holes basic structures ferroelectricity 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 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 Crystals are everywhere! More crystals 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) ? 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 shouldn’t occur. 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 - , , Seven unit cell shapes • • • • • • • Cubic Tetragonal Orthorhombic Monoclinic Triclinic Hexagonal Rhombohedral a=b=c a=bc abc abc abc a=bc a=b=c ===90° ===90° ===90° ==90°, 90° 90° ==90°, =120° ==90° Think about the shapes that these define - look at the models provided. 2D example - rocksalt (sodium chloride, NaCl) We define lattice points ; these are points with identical environments Choice of origin is arbitrary - lattice points need not be atoms - but unit cell size should always be the same. This is also a unit cell it doesn’t matter if you start from Na or Cl - or if you don’t start from an atom This is NOT a unit cell even though they are all the same - empty space is not allowed! In 2D, this IS a unit cell In 3D, it is NOT All M.C. Escher works (c) Cordon Art-Baarn-the Netherlands. All rights reserved. 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!] 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