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# Presentation1

## by jo on Sep 15, 2010

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## Presentation1Presentation Transcript

•
• Crystal Geometry
• Crystals
• Lattice
• Lattice points, lattice translations
• Cell--Primitive & non primitive
• Lattice parameters
• Crystal=lattice+motif
• Matter Crystalline Amorphous Solid Liquid Gas
• Crystal?
• A 3D translationally periodic arrangement of atoms in space is called a crystal.
• Air, Water and Earth A two-dimensional periodic pattern by a Dutch artist M.C. Escher
• Lattice?
• A 3D translationally periodic arrangement of points in space is called a lattice.
• A 3D translationally periodic arrangement of atoms Crystal A 3D translationally periodic arrangement of points Lattice
• What is the relation between the two? Crystal = Lattice + Motif Motif or basis: an atom or a group of atoms associated with each lattice point
• Crystal=lattice+basis Lattice: the underlying periodicity of the crystal, Basis: atom or group of atoms associated with each lattice points Lattice: how to repeat Motif: what to repeat
• + Love Pattern Love Lattice + Heart =
• Formula for Love Potion? Mix one molecule of potassium iodide with two molecules of sulfur KI + 2S = KISS
• Space Lattice
• A discrete array of points in 3-d space such that every point has identical surroundings
• Lattice Finite or infinite?
• Primitive cell Primitive cell Nonprimitive cell
• Cells
• A cell is a finite representation of the infinite lattice
• A cell is a parallelogram (2D) or a parallelopiped (3D) with lattice points at their corners.
• If the lattice points are only at the corners, the cell is primitive.
• If there are lattice points in the cell other than the corners, the cell is nonprimitive.
• Lattice Parameters Lengths of the three sides of the parallelopiped : a, b and c. The three angles between the sides:  ,  , 
• Convention
• a parallel to x -axis
• b parallel to y -axis
• c parallel to z -axis
• Angle between y and z
• Angle between z and x
•  Angle between x and y
• The six lattice parameters a , b , c ,  ,  ,  The cell of the lattice lattice crystal + Motif
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• In order to define translations in 3-d space, we need 3 non-coplanar vectors
• Conventionally, the fundamental translation vector is taken from one lattice point to the next in the chosen direction
• With the help of these three vectors, it is possible to construct a parallelopiped called a CELL
• The smallest cell with lattice points at its eight corners has effectively only one lattice point in the volume of the cell.
• Such a cell is called PRIMITIVE CELL
• Bravais Space Lattices
• Conventionally, the finite representation of space lattices is done using unit cells which show maximum possible symmetries with the smallest size.
• Symmetries: 1.Translation
• 2. Rotation
• 3. Reflection
• Considering
• Maximum Symmetry, and
• Minimum Size
• Bravais concluded that there are only 14 possible Space Lattices (or Unit Cells to represent them). These belong to 7 Crystal Classes
• Arrangement of lattice points in the unit cell
• 8 Corners (P)
• 8 Corners and 1 body centre (I)
• 8 Corners and 6 face centres (F)
• 8 corners and 2 centres of opposite faces (A/B/C)
• Effective number of l.p.
• 5. Hexagonal unit cell has 12 corners of the hexagonal prism 2 centres of hexagonal faces
• Cubic Crystals
• Simple Cubic (P)
• Body Centred Cubic (I) – BCC
• Face Centred Cubic (F) - FCC
• Tetragonal Crystals
• Simple Tetragonal
• Body Centred Tetragonal
• Orthorhombic Crystals
• Simple Orthorhombic
• Body Centred Orthorhombic
• Face Centred Orthorhombic
• End Centred Orthorhombic
• Hexagonal Crystals
• Simple Hexagonal or most commonly HEXAGONAL
• Rhombohedral Crystals
• Rhombohedral (simple)
• Monoclinic Crystals
• Simple Monoclinic
• End Centred Monoclinic (A/B)
• Triclinic Crystals
• Triclinic (simple)
• Crystal Structure
• Space Lattice + Basis (or Motif)
• Basis consists of a group of atoms located at every lattice point in an identical fashion
• To define it, we need to specify
• Number of atoms and their kind
• Internuclear spacings
• Orientation in space
• Atoms are assumed to be hard spheres