کریستالوگرافی بخش تقارن آینه

کریستالوگرافی بخش تقارن آینه

اسلاید 1: موضوع:کریستال گرافی بخش تقارن _آینهنام ارئه دهنده :میلاد جعفری

اسلاید 2: SymmetryMotif: the fundamental part of a symmetric design that, when repeated, creates the whole patternOperation: some act that reproduces the motif to create the patternElement: an operation located at a particular point in space

اسلاید 3: 2-D SymmetrySymmetry Elements1. Rotationa. Two-fold rotation= 360o/2 rotation to reproduce a motif in a symmetrical pattern66A Symmetrical Pattern

اسلاید 4: Symmetry Elements1. Rotationa. Two-fold rotation= 360o/2 rotation to reproduce a motif in a symmetrical pattern= the symbol for a two-fold rotationMotifElementOperation662-D Symmetry

اسلاید 5: 66first operation stepsecond operation step2-D SymmetrySymmetry Elements1. Rotationa. Two-fold rotation= 360o/2 rotation to reproduce a motif in a symmetrical pattern= the symbol for a two-fold rotation

اسلاید 6: Symmetry Elements1. Rotationa. Two-fold rotationSome familiar objects have an intrinsic symmetry2-D Symmetry

اسلاید 7: Symmetry Elements1. Rotationa. Two-fold rotationSome familiar objects have an intrinsic symmetry2-D Symmetry

اسلاید 8: Symmetry Elements1. Rotationa. Two-fold rotationSome familiar objects have an intrinsic symmetry2-D Symmetry

اسلاید 9: Symmetry Elements1. Rotationa. Two-fold rotationSome familiar objects have an intrinsic symmetry2-D Symmetry

اسلاید 10: Symmetry Elements1. Rotationa. Two-fold rotationSome familiar objects have an intrinsic symmetry2-D Symmetry

اسلاید 11: Symmetry Elements1. Rotationa. Two-fold rotationSome familiar objects have an intrinsic symmetry2-D Symmetry

اسلاید 12: Symmetry Elements1. Rotationa. Two-fold rotationSome familiar objects have an intrinsic symmetry180o rotation makes it coincidentWhat’s the motif here??Second 180o brings the object back to its original position2-D Symmetry

اسلاید 13: Symmetry Elements1. Rotationb. Three-fold rotation= 360o/3 rotation to reproduce a motif in a symmetrical pattern6662-D Symmetry

اسلاید 14: 666step 1step 2step 32-D SymmetrySymmetry Elements1. Rotationb. Three-fold rotation= 360o/3 rotation to reproduce a motif in a symmetrical pattern

اسلاید 15: Symmetry Elements1. Rotation66666666666666661-fold2-fold3-fold4-fold6-fold9tdZ5-fold and > 6-fold rotations will not work in combination with translations in crystals (as we shall see later). Thus we will exclude them now.aidentityObjects with symmetry:2-D Symmetry

اسلاید 16: 4-fold, 2-fold, and 3-fold rotations in a cubeClick on image to run animation

اسلاید 17: Symmetry Elements2. Inversion (i)inversion through a center to reproduce a motif in a symmetrical pattern= symbol for an inversion centerinversion is identical to 2-fold rotation in 2-D, but is unique in 3-D (try it with your hands)662-D Symmetry

اسلاید 18: Symmetry Elements3. Reflection (m)Reflection across a “mirror plane” reproduces a motif = symbol for a mirror plane2-D Symmetry

اسلاید 19: We now have 6 unique 2-D symmetry operations: 1 2 3 4 6 m Rotations are congruent operations reproductions are identicalInversion and reflection are enantiomorphic operationsreproductions are “opposite-handed”2-D Symmetry

اسلاید 20: Combinations of symmetry elements are also possibleTo create a complete analysis of symmetry about a point in space, we must try all possible combinations of these symmetry elementsIn the interest of clarity and ease of illustration, we continue to consider only 2-D examples2-D Symmetry

اسلاید 21: Try combining a 2-fold rotation axis with a mirror2-D Symmetry

اسلاید 22: Try combining a 2-fold rotation axis with a mirrorStep 1: reflect(could do either step first)2-D Symmetry

اسلاید 23: Try combining a 2-fold rotation axis with a mirrorStep 1: reflectStep 2: rotate (everything)2-D Symmetry

اسلاید 24: Try combining a 2-fold rotation axis with a mirrorStep 1: reflectStep 2: rotate (everything)Is that all??2-D Symmetry

اسلاید 25: Try combining a 2-fold rotation axis with a mirrorStep 1: reflectStep 2: rotate (everything)No! A second mirror is required2-D Symmetry