Review of Crystallography 1 Crystal basics m 1 Crvstal basic 1. Crystal ■2 Symmetry 2. Fundamental Characteristics of Crystals 3 Crystal Structure Analysis n 4 Crystal Chemistry E 5 Some Important Crystal Structures Why Solids? Early Ideas 6 ALL Compounds are solids under suitable nditions of temperature and pressure. Many exist o Crystals are solid -but solids are not necessarily crystalline o Crystals have symmetry(Kepler, 1611) and long o atoms in -fixed position range order I"simple"case- crystalline solid= Crystal Structure apes can be pa ked produce regular shapes (Hooke; Hauy, 1812) Why study crystal structures o description of solid n with other similar materials- 费 o correlation with physical properties Crystallinity Definition-Crvstal aA crystal may be defined as a collection of ator arranged in a pattern that is periodie in 3D. Crystals- A homogenous solid formed by a rily solids, but not all solids ar repeating, threedimensional pattern of crystalline(amorphous solids lack long range periodic atoms, Ions, or 1 molecules and having fixed order distances between constituent parts In a perfect single crystal, all atoms in the crystal are related either through translational symmetry or point symmetry POlycrystalline materials are made up of a great number of tiny ( m to nm) single crystals &Crystalline solids can be divided into two categorie extended and molecular
1 Review of Crystallography 1 Crystal Basics 2 Symmetry 3 Crystal Structure Analysis 4 Crystal Chemistry 5 Some Important Crystal Structures 1 Crystal Basics 1.Crystal 2.Fundamental Characteristics of Crystals Why Solids? µ ALL Compounds are solids under suitable conditions of temperature and pressure. Many exist only as solids. µ atoms in ~fixed position “simple”case ¾ crystalline solid Þ Crystal Structure Why study crystal structures? µ description of solid µ comparison with other similar materials ¾ classification µ correlation with physical properties Early Ideas Crystals are solid ¾ but solids are not necessarily crystalline Crystals have symmetry (Kepler, 1611) and long range order Spheres and small shapes can be packed to produce regular shapes (Hooke; Hauy,1812) ? Definition ¾ Crystal Crystals ¾ A homogenous solid formed by a repeating, three-dimensional pattern of atoms, ions, or molecules and having fixed distances between constituent parts. Crystallinity A crystal may be defined as a collection of atoms arranged in a pattern that is periodic in 3D. Crystals are necessarily solids, but not all solids are crystalline (amorphous solids lack long range periodic order). In a perfect single crystal, all atoms in the crystal are related either through translational symmetry or point symmetry. Polycrystalline materials are made up of a great number of tiny (mm to nm) single crystals Crystalline solids can be divided into two categories extended and molecular
Single Crystal and Single crystals Polycrystalline Materials array over the entire extent of the material ted arrangemen throughout the specim ment of atoms extends alline material: comprised of m ve different p all unit cells have the same orientation crystallographic orientation. There exist atomic n exist in nature mismatch within the regions where grains meet e can also be grown (eg. Si e without external constraints. will have flat gular faces Beautiful Crystals Polycrystalline Materials s Crystals of different 鲁s1Zes Grain Boundaries -mismatch between two ighboring crystals Polycrystalline Materials Basic Characteristic of Crystals OMost crystalline materials are composed of many a Homogeneity-Under macro small crystals called grains observation, the physics effect and chemical CRystallographic directions of adjacent grains are of a cry ire the usually random Anisot Physical properties of a CThere is usually atomic mismatch where two crystal differ according to the direction of grains meet -this is called a grain boundary measurement Most powdered materials have many randomly oriented grains
2 Single Crystal and Polycrystalline Materials ß Single crystal:atoms are in a repeating or periodic array over the entire extent of the material ß Polycrystalline material: comprised of many small crystals or grains. The grains have different crystallographic orientation.There exist atomic mismatch within the regions where grains meet. These regions are called grain boundaries. Single Crystals repeated arrangement of atoms extends throughout the specimen all unit cells have the same orientation exist in nature can also be grown (eg. Si) without external constraints, will have flat, regular faces Beautiful Crystals Polycrystalline Materials Crystals of different sizes orientations shapes Grain Boundaries -mismatch between two neighboring crystals Polycrystalline Materials Most crystalline materials are composed of many small crystals called grains Crystallographic directions of adjacent grains are usually random There is usually atomic mismatch where two grains meet ¾¾ this is called a grain boundary Most powdered materials have many randomly oriented grains Basic Characteristic of Crystals Homogeneity ¾¾ Under macroscopic observation,the physics effect and chemical composition of a crystal are the same. Anisotropy ¾¾ Physical properties of a crystal differ according to the direction of measurement
Anisotropy different packing. For instance, atoms along the edge of FCC unit cell are orie tame p l re rta lime mo berk a tenin properties of crysta tals. for instance. tI properties are isotropic. deformation depends on the directio iSome polycrystalline materials have grains n which a stress is applied. with preferred orientations(texture). so properties are dominated by those relevant to the texture orientation and the material exhibits anisotropic properties Law of Constancy of Interfacial Angle Crystal Shape sThe interfacial angles are constant for all IThe external shape of a crystal is referred to as its crystals if a given mineral with identical mposition at the same temperature eSince all crystals of the same substance will Typically see faces on crystals grown fron t E Not all crystals have well defined external faces have the same spacing between lattice points solution (they have the same crystal structure), the I Natural faces always have low indices(orientation sponding faces of the same can be described by Miller indices that are small mineral will be the same sThe symmetry of the lattice will determine the tThe faces that you see are the lowest energy faces angular relationships between crystal faces. Surface energy is minimized during growth This is a term that refers to the form that a crystal Crystal Habits takes as it grows pRismatic Crystal Habit Tabular rHombohedra dOdecahedral
3 Anisotropy Different directions in a crystal have different packing. For instance, atoms along the edge of FCC unit cell are more separated than along the face diagonal. This causes anisotropy in the properties of crystals, for instance, the deformation depends on the direction in which a stress is applied. In some polycrystalline materials, grain orientations are random, so bulk material properties are isotropic. Some polycrystalline materials have grains with preferred orientations (texture), so properties are dominated by those relevant to the texture orientation and the material exhibits anisotropic properties. Law of Constancy of Interfacial Angle The interfacial angles are constant for all crystals if a given mineral with identical composition at the same temperature. Since all crystals of the same substance will have the same spacing between lattice points (they have the same crystal structure), the angles between corresponding faces of the same mineral will be the same. The symmetry of the lattice will determine the angular relationships between crystal faces. Crystal Shape The external shape of a crystal is referred to as its Habit Not all crystals have well defined external faces Typically see faces on crystals grown from solution Natural faces always have low indices (orientation can be described by Miller indices that are small integers) The faces that you see are the lowest energy faces Surface energy is minimized during growth This is a term that refers to the form that a crystal takes as it grows. Prismatic Pyramidal Tabular Rhombohedra Dodecahedral Acicular Bladed Crystal Habits Crystal Habits
Law of Symmetry aLaw of Symmetry: Only 1, 2, 3, 4, 6 fold rotatio axis can exist in crystal Why snowflakes have 6 corners, never 5 or 7? 多3 By considering the packing of polygons in 2 dimensions, demonstrate why pentagons and Allowed Quasicrystal Structures(First in 1984) rotation a RoomMgoazno.s Ro Mgo. cde NOT 5.>6 Face-centred icosahedral R-Mg-Zn Primitiv Quasicrystal: AlFe Cu e P Dodecahedral morphology Rhombic triacontahedral Quasicrystalline Materials Amorphous solids bNon-periodic long-range ordered structures nIdeal solid crystals exhibits structural long range Rotational symmetry of diffraction patterns (e. order (LRO) FReal crystals contain imperfections, i.e., defects and impurities, which spoil the lRo AMorphous solids lack any LRO Ithough may exhibit short range order (SRO) Crystal ) Gas
4 Law of Symmetry Law of Symmetry: Only 1,2,3,4,6-fold rotation axis can exist in crystal. Why snowflakes have 6 corners, never 5 or 7? By considering the packing of polygons in 2 dimensions, demonstrate why pentagons and heptagons shouldn ’t occur. Empty space not allowed Quasicrystal: AlFeCu Allowed rotation axis: 1, 2, 3, 4, 6 NOT 5, > 6 Quasicrystal Structures (First in 1984) R0.09Mg0.34Zn0.57 Dodecahedral morphology R0.1Mg0.4Cd0.5 Rhombic triacontahedral morphology ED: 5 fold axis Face-centred icosahedral R-Mg-Zn Primitive icosahedral R-Mg-Cd Non-periodic long-range ordered structures Rotational symmetry of diffraction patterns (e.g. 5-fold, 10-fold) impossible for periodic crystals Quasicrystalline Materials Quasi-unit cells Amorphous Solids Ideal solid crystals exhibits structural long range order (LRO) Real crystals contain imperfections, i.e., defects and impurities, which spoil the LRO Amorphous solids lack any LRO [though may exhibit short range order (SRO)] Crystal Glass (amorphous) Gas
Quartz Crystal and Quartz Glass Transparent, amorphous solid Composition almost all silicon dioxide(SiO Quartz sand) Lead glass SiO.+ PbO, and K Quartz Crystal Quartz Glass Pyrex glass ? SiOz with BD3 so so% Green glass(cheap bottles)) FeO Blue glass Cobalt oxide+ Siog Fo mu ne Violet glass→ Yellow glass Uranium oxide SiO2 Red glass ]Gold and copper+ SiO 2 Liquid crystal From Crystal to Liquid Crystal Liquid crystals are a phase to Liquid tween that 捷图 LC typically rodshaped organic moieties about 25 湖鬻 Angstroms in length and liquid This is the structure change process of some molecule saiid tisd Orlat with long chains when increasing temperatures Principles of Liquid Crystal Displays +1 Entropy
5 Quartz Crystal and Quartz Glass Quartz Crystal Quartz Glass Glass ß Transparent, amorphous solid –Composition almost all silicon dioxide (SiO2 – Quartz sand) ß Ordinary glass ‡ 75% SiO2 ß Pyrex glass ‡ SiO2 with B2O3 ß Lead glass ‡ SiO2 + PbO, and K2O ß Green glass (cheap bottles) ‡ FeO + SiO2 ß Blue glass ‡ Cobalt oxide + SiO2 ß Violet glass ‡ Manganese + SiO2 ß Yellow glass ‡ Uranium oxide + SiO2 ß Red glass ‡ Gold and copper + SiO2 Liquid Crystal Liquid crystals are a phase of matter whose order is intermediate between that of a liquid and that of a crystal. The molecules are typically rod-shaped organic moieties about 25 Angstroms in length and their ordering is a function of temperature. From Crystal to Liquid Crystal to Liquid (a)crystal，(b)、(c) anisotropic liquids，(d) isotropic liquid This is the structure change process of some molecules with long chains when increasing temperatures Nematic Entropy driven formation of liquid crystals of rod-like colloids Isotropic Crystal Smectic = Direction of increasing density Principles of Liquid Crystal Displays No voltage voltage