Transcription of Geometry of Crystals - Stanford University
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Geometry of Crystals - Stanford University
Geometry of CrystalsCrystal is a solid composed of atoms, ions or molecules that demonstrate long range periodic order in three dimensionsThe Crystalline StateState of MatterFixed VolumeFixed ShapeOrderPropertiesGasNoNoNoIsotropicLi quidYesNoShort-rangeIsotropicSolid (amorphous)YesYesShort-rangeIsotropicSol id (crystalline)YesYesLong-rangeAnisotropic Crystal LatticeNot only atom, ion or molecule positions are repetitious there are certain symmetry relationships in their constantsa, bCrystallinestructure=Basis+LatticeabABC A tomsCrystal LatticeaOne-dimensional lattice with lattice parameter aaaru abTwo-dimensional lattice with lattice parameters a,band ab bar uCrystal Latticecbarwu Crystal LatticeLattice vectors, lattice parameters and interaxial angles Lattice vectorabcLattice parameterabcInteraxial angle bacabcA lattice is an array of points in space in which the environment of each point is identicalCrystal LatticeLatticeNot a latticeCrystal LatticeUnit cell content Coordinates of all atoms Types of atoms Site occupancy Individual displacement parameters0x1x2x3y1y2y3 Crystal LatticeUsually unit cell has more than one molecule or group of atoms They can be represented by symmetry operatorsrotationSymmetrySymmetry is a property of a crystal which is used to describe repetitions of a pattern within that is done using symmetry operatorsTranslationORotation(about axis O) = 360 /nwhere nis the foldof the axisn= 1, 2, 3, 4
Lattice vectors, lattice parameters and interaxial angles Lattice vector a b c Lattice parameter a b c Interaxial angle b a c a b c A lattice is an array of points in space in which the environment of each point is identical. Crystal Lattice ... When X-rays diffract
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