crystallogeaphy

Empirical Formula C19H19N3O10 Formula weight 449.37 Temperature 100(2) K Wave length 0.71073 Å Crystal system Triclinic Space group Pī   Unit cell dimensions a = 8.7689(9) Å a= 101.408(5)°. b =10.5701(12) Å b= 95.301(5)°. c = 11.911(2) Å g = 113.633(5)°. Volume 973.1(2) Å 3 Z 2 Density(calculated) 1.534 Mg/m3 Absorption coefficient 0.126 mm-1 F(000) 468 Crystal size 0.30×0.25×0.25 mm3 Theta range for data collection 1.78 to 29.00° Index ranges -11<=h<11,-14<=k<=14,-16<=1<=16 Reflections collected 11866 Independent reflecions 5169 [R(int)=0.0263] Completmeness to theta=29.00° 99.8% Refinement method Full-matrix least-squares on F2 Data / restraints / parameters 5169 / 0 / 289 Goodness-of-fit on F2 1.003 Final R indices [for 4098 rfln with I>2sigma(I)] R1= 0.0410, wR2=0.0993 R indices (all data) R1=0.0552, wR2=0.1088 Larges diff. peak and hole 0.388 and-0.305 e. Å -3

جدول3-2 برخی از طول(Å)،زاویه های پیوندی(°) و زاویه های پیچشی(°)ترکیب هم بلور pydcH2).4H2O)( ( phen-dione N(1)-C(2) 1.3403(17) N(3)-C(17) 1.3342(17) N(1)-C(1) 1.3439(16) N(3)-C(13) 1.3378(17) O(1)-C(6) 1.2165(16) O(3)-C(18) 1.3181(17) C(1)-C(12) 1.4873(18) O(4)-C(18) 1.2176(17) N(2)-C(11) O(5)-C(19) 1.2134(17) N(2)-C(12) 1.3411(17) O(6)-C(19) 1.3175(17) O(2)-C(7) 1.2127(16) C(13)-C(18) 1.5027(19) C(6)-C(7) 1.5399(19) C(17)-C(19) 1.5060(18) C(2)-N(1)-C(1) 117.83(12) O(2)-C(7)-C(8) 123.50(13) N(1)-C(1)-C(5) 121.74(12) O(2)-C(7)-C(6) 118.64(12) N(1)-C(1)-C(12) 117.27(11) N(2)-C(11)-C(10) 123.86(13) C(11)-N(2)-C(12) 117.65(11) N(2)-C(12)-C(8) 122.48(12) N(1)-C(2)-C(3) 124.03(12) N(2)-C(12)-C(1) 116.67(11) O(1)-C(6)-C(5) 122.90(12) C(17)-N(3)-C(13) 117.54(11) O(1)-C(6)-C(7) 118.75(12) N(3)-C(13)-C(18) 115.52(12) C(5)-C(6)-C(7) 118.32(11) N(3)-C(17)-C(19) 114.09(11) C(2)-N(1)-C(1)-C(5) -0.34(19) C(7)-C(8)-C(12)-N(2) -175.51(12) C(2)-N(1)-C(1)-C(12) -179.67(12) N(1)-C(1)-C(12)-N(2) -1.89(18) C(1)-N(1)-C(2)-C(3) 1.1(2) C(5)-C(1)-C(12)-N(2) 178.79(12) N(1)-C(2)-C(3)-C(4) -0.5(2) N(1)-C(1)-C(12)-C(8) 178.11(12) N(1)-C(1)-C(5)-C(4) -1.1(2) C(17)-N(3)-C(13)-C(14) 0.2(2) N(1)-C(1)-C(5)-C(6) 177.60(12) C(17)-N(3)-C(13)-C(18) 179.95(12) C(4)-C(5)-C(6)-O(1) 4.8(2) N(3)-C(13)-C(14)-C(15) C(1)-C(5)-C(6)-O(1) -173.87(13) C(13)-N(3)-C(17)-C(16) -0.3(2) O(1)-C(6)-C(7)-O(2) -0.8(2) C(13)-N(3)-C(17)-C(19) -179.74(12) C(5)-C(6)-C(7)-O(2) -178.73(13) C(15)-C(16)-C(17)-N(3) -0.1(2) O(1)-C(6)-C(7)-C(8) 177.16(12) N(3)-C(13)-C(18)-O(4) 173.28(13) O(2)-C(7)-C(8)-C(9) -2.8(2) C(14)-C(13)-C(18)-O(4) -7.0(2) O(2)-C(7)-C(8)-C(12) 174.42(13) N(3)-C(13)-C(18)-O(3) -6.35(19) C(12)-N(2)-C(11)-C(10) 0.4(2) C(14)-C(13)-C(18)-O(3) 173.38(13) C(9)-C(10)-C(11)-N(2) 1.4(2) N(3)-C(17)-C(19)-O(5) 2.7(2) C(11)-N(2)-C(12)-C(8) -1.96(19) C(16)-C(17)-C(19)-O(5) -176.81(14) C(11)-N(2)-C(12)-C(1) 178.03(12) N(3)-C(17)-C(19)-O(6) -177.54(12) C(9)-C(8)-C(12)-N(2) 1.8(2) C(16)-C(17)-C(19)-O(6) 2.98(19)

Objectives By the end of this section you should: be able to identify a unit cell in a symmetrical pattern know that there are 7 possible unit cell shapes be able to define cubic, tetragonal, orthorhombic and hexagonal unit cell shapes Crystal Structure

LIQUIDS and LIQUID CRYSTALS matter Matter GASES LIQUIDS and LIQUID CRYSTALS SOLIDS Crystal Structure

Gases Gases have atoms or molecules that do not bond to one another in a range of pressure, temperature and volume. These molecules haven’t any particular order and move freely within a container. Crystal Structure

Liquids and Liquid Crystals Similar to gases, liquids haven’t any atomic/molecular order and they assume the shape of the containers. Applying low levels of thermal energy can easily break the existing weak bonds. Liquid crystals have mobile molecules, but a type of long range order can exist; the molecules have a permanent dipole. Applying an electric field rotates the dipole and establishes order within the collection of molecules. + - Crystal Structure

Crytals Solids consist of atoms or molecules executing thermal motion about an equilibrium position fixed at a point in space. Solids can take the form of crystalline, polycrstalline, or amorphous materials. Solids (at a given temperature, pressure, and volume) have stronger bonds between molecules and atoms than liquids. Solids require more energy to break the bonds. Crystal Structure

ELEMENTARY CRYSTALLOGRAPHY Crystal Structure

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Crystal Geometry Crystals Lattice Lattice points, lattice translations Cell--Primitive & non primitive Lattice parameters Crystal=lattice+motif Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Types of Solids Single crsytal, polycrystalline, and amorphous, are the three general types of solids. Each type is characterized by the size of ordered region within the material. An ordered region is a spatial volume in which atoms or molecules have a regular geometric arrangement or periodicity. Crystal Structure

Crystalline Solid Crystalline Solid is the solid form of a substance in which the atoms or molecules are arranged in a definite, repeating pattern in three dimension. Single crystals, ideally have a high degree of order, or regular geometric periodicity, throughout the entire volume of the material. Crystal Structure

Crystalline Solid Single crystal has an atomic structure that repeats periodically across its whole volume. Even at infinite length scales, each atom is related to every other equivalent atom in the structure by translational symmetry Single Pyrite Crystal Amorphous Solid Single Crystal Crystal Structure

Polycrystalline Solid Polycrystal is a material made up of an aggregate of many small single crystals (also called crystallites or grains). Polycrystalline material have a high degree of order over many atomic or molecular dimensions. These ordered regions, or single crytal regions, vary in size and orientation wrt one another. These regions are called as grains ( domain) and are separated from one another by grain boundaries. The atomic order can vary from one domain to the next. The grains are usually 100 nm - 100 microns in diameter. Polycrystals with grains that are <10 nm in diameter are called nanocrystalline Polycrystalline Pyrite form (Grain) Crystal Structure

Amorphous Solid Amorphous (Non-crystalline) Solid is composed of randomly orientated atoms , ions, or molecules that do not form defined patterns or lattice structures. Amorphous materials have order only within a few atomic or molecular dimensions. Amorphous materials do not have any long-range order, but they have varying degrees of short-range order. Examples to amorphous materials include amorphous silicon, plastics, and glasses. Amorphous silicon can be used in solar cells and thin film transistors. Crystal Structure

Departure From Perfect Crystal Strictly speaking, one cannot prepare a perfect crystal. For example, even the surface of a crystal is a kind of imperfection because the periodicity is interrupted there. Another example concerns the thermal vibrations of the atoms around their equilibrium positions for any temperature T>0°K. As a third example, actual crystal always contains some foreign atoms, i.e., impurities. These impurities spoils the perfect crystal structure. Crystal Structure

CRYSTALLOGRAPHY What is crystallography? The branch of science that deals with the geometric description of crystals and their internal arrangement. Crystal Structure

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Crystal? Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi A 3D translationally periodic arrangement of atoms in space is called a crystal. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi A two-dimensional periodic pattern by a Dutch artist M.C. Escher Air, Water and Earth Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Lattice? Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi A 3D translationally periodic arrangement of points in space is called a lattice. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Crystal Lattice A 3D translationally periodic arrangement of atoms A 3D translationally periodic arrangement of points Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

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 Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

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 Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Love Pattern = Love Lattice + Heart + Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Space Lattice A discrete array of points in 3-d space such that every point has identical surroundings Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Lattice Finite or infinite? Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Nonprimitive cell Primitive cell Primitive cell Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi 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. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Lattice Parameters Lengths of the three sides of the parallelopiped : a, b and c. The three angles between the sides: , ,  Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi 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 Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

The six lattice parameters a, b, c, , ,  The cell of the lattice lattice + Motif crystal Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi 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 Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi With the help of these three vectors, it is possible to construct a parallelopiped called a CELL Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi 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 Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

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 Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi 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 Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

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. Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi 5. Hexagonal unit cell has 12 corners of the hexagonal prism 2 centres of hexagonal faces Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Cubic Crystals Simple Cubic (P) Body Centred Cubic (I) – BCC Face Centred Cubic (F) - FCC Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Tetragonal Crystals Simple Tetragonal Body Centred Tetragonal Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Orthorhombic Crystals Simple Orthorhombic Body Centred Orthorhombic Face Centred Orthorhombic End Centred Orthorhombic Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Hexagonal Crystals Simple Hexagonal or most commonly HEXAGONAL Rhombohedral Crystals Rhombohedral (simple) Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi Monoclinic Crystals Simple Monoclinic End Centred Monoclinic (A/B) Triclinic Crystals Triclinic (simple) Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi 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 Shiv K. Gupta Department of Applied Mechanics, IIT Delhi

Shiv K. Gupta Department of Applied Mechanics, IIT Delhi