Chapter 3 Slides

Chapter 3 Slides - Chapter 3 1st lecture on Chapter 3 The...

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Chapter 3 1 st lecture on 01-17-08
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Chapter 3 Chapter 3 The Structure of Crystalline Solids (Metals) The Structure of Crystalline Solids (Metals) and a glance at Amorphous Solids and a glance at Amorphous Solids • Why study the structure? – The properties determine the microstructure!
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Recent work Recent work and its follow on and its follow on • Ch. 2 was about bonding – Now we consider one aspect of this – bonding in the solid state • Many interesting aspects of this for electronic properties – For now we concentrate on setting up an understanding of the structural and mechanical properties • 3 principal metallic crystal structures – Fcc, hcp and bcc • Notation for describing planes and directions in the lattice • Single crystals – and polycrystals • Structure determination by diffraction
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Face Face - - Centered Cubic Centered Cubic fcc fcc (1) (1) Hard shell (overlapping closed electron shell) model of packing in one unit cell of the fcc crystal structure (a) (packing spheres) The lattice of points that repeats regularly in 3D to give long range order (LRO) is shown in (b) A bigger hard shell model showing many unit cells is shown in (c) – The LRO is clear – The cubic symmetry is clear – Where atoms touch is clear, as are directions along which they do NOT touch Picture (a) is more physically correct than (b) but (b) allows the atom positions to be better visualized Each atom is touched by 12 other atoms, making its coordination number (CN) 12
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Face Face - - Centered Cubic Centered Cubic fcc fcc (2) (2) Atoms touch along the face diagonal The lattice parameter a in terms of the atom diameter (2R) is a = 2R 2 Each corner atom is shared by 8 unit cells Each face-centered atom is shared by 2 until cells Thus (8x1/8) + (6x1/2) = 4 atoms per unit cell The atomic packing factor is then the volume of 4 atoms (4 x 4/3 π r 3 )/a 3 = 0.74 No higher packing exists for spherical atoms that are all the same size! Example prob. 3.3 computes the mass density of Cu knowing the atomic weight and the structure and lattice parameter Cu, Ag, Au and Pb are some of the elements having the fcc structure
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The body The body - - centered cubic crystal centered cubic crystal structure (bcc) structure (bcc) Atoms touch along the cell diagonal – a = 4R/ 3 Each corner atom is again shared with 8 other cells, but the central atom belongs only to one cell - # of atoms per unit cell is (8x1/8) + (1x1) = 2 Like fcc, the atoms do NOT touch along the cube edges
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This note was uploaded on 04/20/2008 for the course EML 3234 taught by Professor Hellstrom during the Spring '08 term at FSU.

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Chapter 3 Slides - Chapter 3 1st lecture on Chapter 3 The...

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