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- 1. CRYSTAL STRUCTURE Presentation by: MOHAMMED NASRULLA BASHA Mechanical Engineering DON BOSCO IT
- 2. Space Lattice & Unit Cell A space lattice is simply a set of points each of which has identical surroundings. OR A Geometrical representation of the crystal structure in terms of lattice points is called space lattice, which has the property that the distribution or placement of lattice points that surrounds any given lattice point, remains throughout the crystal. 3D space Lattice
- 3. The most fundamental property of a crystal lattice is its symmetry Space Lattice & Unit Cell A square lattice may be visualized like this. Rectangles Hexagons
- 4. Space Lattice & Unit Cell There are an essentially infinite number of unit cells possible. For example, a square and hexagonal unit cell may contain any of the following object patterns.
- 5. Space Lattice & Unit Cell 3D View SIMPLE BODY CENTERED FACE CENTERED Click on objects to Animate them
- 6. Bravais Lattices There are fourteen distinct space groups that a Bravais lattice can have. Thus, from the point of view of symmetry, there are fourteen different kinds of Bravais lattices. Auguste Bravais (1811-1863) was the first to count the categories correctly.
- 7. Bravais Lattices Simple Cubic Simple Face Centered Body Centered a1 = a2 = a3 α = β = γ = 90o Click on objects to Animate them
- 8. Bravais Lattices TETRAGONAL Simple Tetragonal Body Centered Tetragonal a1 = a2 ≠ a3 α = β = γ = 90o
- 9. Bravais Lattices ORTHORHOMBIC Simple Orthorhombic Base Centered Orthorhombic Body Centered orthorhombic Face Centered Orthorhombic a1 ≠ a2 ≠ a3 α = β = γ = 90o
- 10. Bravais Lattices MONOCLINIC Simple Monoclinic Base Centered Monoclinic a1 ≠ a2 ≠ a3 α = γ = 90o ≠ β
- 11. Bravais Lattices TRICLINIC a1 ≠ a2 ≠ a3 α ≠ β ≠ γ
- 12. Bravais Lattices RHOMBOHYDRAL (TRIGONAL) a1 = a2 = a3 α = β = γ < 120o , ≠ 90o
- 13. Bravais Lattices HEXAGONAL a1 = a2 ≠ a3 α = β = 90o , γ = 120o
- 14. Miller Indices are a method of describing the orientation of a plane or set of planes within a lattice in relation to the unit cell. They were developed by William Hallowes Miller . These indices are useful in understanding many phenomena in materials science, such as explaining the shapes of single crystals, the form of some materials' microstructure, the interpretation of X-ray diffraction patterns, and the movement of a dislocation , which may determine the mechanical properties of the material. Miller Indices
- 15. Miller Indices
- 16. Miller Indices
- 17. Miller Indices <ul><li>How to index a lattice plane </li></ul>
- 18. Miller Indices <ul><li>How to draw a lattice plane </li></ul>
- 19. Miller Indices <ul><li>Parallel lattice planes </li></ul><ul><li>Equation for Inter planar spacing. </li></ul>
- 20. Miller Indices <ul><li>Planes related by Symmetry </li></ul>
- 21. If we take the NaCl unit cell and remove all the red Cl ions, we are left with only the blue Na. If we compare this with the fcc / ccp unit cell, it is clear that they are identical. Thus, the Na is in a FCC sub lattice. Sodium Chloride (NaCl)

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