Crystal Structures PDF

Basic Concepts of Crystal Structures Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. A phase is a homogeneous part of the system in contact with other parts of the system but separated from them by a well-defined boundary. 3 Ph...

Basic Concepts of Crystal Structures Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. A phase is a homogeneous part of the system in contact with other parts of the system but separated from them by a well-defined boundary. 3 Phases Gas phase – water vapor Liquid phase - water Solid phase - ice  Generally, intermolecular forces are much weaker than intramolecular forces. Intermolecular Forces Intermolecular forces are attractive forces between molecules, while intramolecular forces hold atoms together in a molecule. Intermolecular vs Intramolecular “Measure” of intermolecular force 41 kJ to vaporize 1 mole of water (inter) boiling point melting point 930 kJ to break all O-H bonds in 1 mole of water (intra) ∆Hvap (L  G) ∆Hfus (S  L) ∆Hsub (G  S) Intermolecular Forces Dipole-Dipole Forces Attractive forces between polar molecules Intermolecular Forces Ion-Dipole Forces Attractive forces between an ion and a polar molecule Intermolecular Forces Dispersion Forces Attractive forces that arise as a result of temporary dipoles induced in atoms or ion-induced dipole molecules interaction dipole-induced dipole interaction  Dispersion forces usually increase with molar mass. Intermolecular Forces Dispersion Forces Polarizability is the ease with which the electron distribution in the atom or molecule can be distorted. Polarizability increases with: greater number of electrons more diffuse electron cloud  Intermolecular Forces Hydrogen Bond The hydrogen bond is a special dipole-dipole interaction between they hydrogen atom in a polar N-H, O-H, or F-H bond and an electronegative O, N, or F atom. A H… B or A H… A A & B are N, O, or F Why is the hydrogen bond considered a “special” dipole-dipole interaction? Decreasing molar mass Decreasing boiling point  Solids: Crystalline vs. Amorphous Uniform arrangement of Random arrangement of atoms, ions, or molecules atoms, ions, or molecules Have a sharp melting point Have a wide range of melting point Anisotropic Isotropic Amorphous solids Crystalline solids  Unit cell The basic repeating structural unit of a crystalline solid Each sphere represents an atom, ion, or molecule and is called a lattice point Types of unit cells Unit cell packing Simple cubic cell (scc) 1/8 atom Simplest packing is just layering at 8 spheres directly on top of one another corners 1 particle per unit cell 52% of space occupied by particles Coordination number = 6 *per sphere is in contact with 6 other atoms Unit cell packing Body-centered cubic cell (bcc) 1 atom in center second layer of spheres fits into the 1/8 atom depressions of the first layer and the third at 8 layer into the depressions of the second layer corners 2 particles per unit cell 68% of space occupied by particles Coordination number = 8 *per sphere is in contact with 8 other atoms https://departments.kings.edu/chemlab/chemlab_v2/cscl.html Unit cell packing 1/2 atom Face-centered cubic cell (fcc) on 6 faces spheres at the center of each of the six 1/8 atom faces of the cube at 8 corners 4 particles per unit cell 74% of space occupied by particles Coordination number = 12 *per sphere is in contact with 12 other atoms https://departments.kings.edu/chemlab/chemlab_v2/nacl.html  Unit cell packing Every unit cell in a crystalline solid is adjacent to other unit cells, most of a cell’s atoms are shared by neighboring cells. https://departments.kings.edu/chemlab/chemlab_v2/clospack.html Simple cubic Body-centered cubic Face-centered cubic 1 atom/unit cell 2 atoms/unit cell 4 atoms/unit cell (8 x 1/8 = 1) (8 x 1/8 + 1 = 2) (8 x 1/8 + 6 x 1/2 = 4) Closest packing A The most efficient arrangement of spheres Place next layer here First layer: placed close to each other Second layer: placed in the depressions A of the 1st layer B Closest packing Third layer: A Hexagonal close-packed (hcp, ABA arrangement): placed in the depressions of the 2nd layer, in B line with atoms from 1st layer Cubic close-packed A (ccp, ABC arrangement): A placed in the depressions of the 2nd layer, in line with depressions from 1st layer B C B Closest packing Cubic close-packed structure Hexagonal close-packed structure (Face-centered cubic cell (fcc)) (ABABABABA… layering) ABCABCABCABC… layering A A B B C A A 6 particles per unit 4 particles per unit Coordination number = 12 Coordination number = 12 Crystal structures of metals Difference in crystal structure formation of related elements Formation of crystal structures is based on intermolecular forces needed to produce stable crystal structures e.g.) most stable form of Mg solid is achieved with hcp Relationship between the atomic radius and the edge length in 3 different unit cells Relationship between the atomic radius and the edge length in 3 different unit cells Example Gold (Au) crystallizes in a cubic close-packed structure (the face- centered cubic unit cell) and has a density of 19.3 g/cm3. Calculate the atomic radius of gold in picometers. 1/2 atom on 6 faces Remember: volume (V) = a3 4 particles in 1 unit cell 1/8 atom at 8 corners Example Gold (Au, MM = 197.0 g/mol) crystallizes in a cubic close- packed structure (the face-centered cubic unit cell) and has a density of 19.3 g/cm3. Calculate the atomic radius of gold in picometers. Example Example X-ray diffraction The scattering of X-rays by the units of a crystalline solid An X-ray diffraction pattern is the result of interference in the waves associated with X-rays X rays are scattered by electrons  electron density map BC + CD = 2d sinθ = nλ (Bragg Equation) Example X rays of wavelength 0.154 nm are diffracted from a crystal at an angle of 14.170. Assuming that n = 1, what is the distance (in pm) between layers in the crystal? nλ = 2d sin θ n=1 θ = 14.170 λ = 0.154 nm = 154 pm nλ 1 x 154 pm d= = = 314.0 pm 2sinθ 2 x sin14.17 Uses of X-ray diffraction Accurate determination of bond angle and length of molecules Uses of X-ray diffraction Structural determination of molecules and compounds Uses of X-ray diffraction Structural determination of macromolecules like protein Types of Crystals: Ionic Crystals They are composed of charged species bound by ionic forces or electrostatic attraction Anions and cations are generally quite different in size High melting points due to strength of ionic bonds NaCl Hard and brittle -fcc Poor conductor of heat and electricity Types of Crystals: Ionic Crystals CsCl ZnS -scc -fcc (zincblende) S2- Zn2+  Types of Crystals: Covalent Crystals Atoms are held together in an extensive three-dimensional network entirely by covalent bonds Hard, high melting point Graphite Diamond - Carbon is bonded to 3 - Carbon is bonded to 4 other atoms (sp2) other atoms (sp3) Layers can slide over one another Types of Crystals: Molecular Crystals The lattice points are occupied by molecules, and the attractive forces between them are van der Waals forces and/or hydrogen bonding Soft, low melting point Poor conductor of heat and electricity Types of Crystals: Metallic Crystals Every lattice point in a crystal is occupied by an atom of the same metal. Soft to hard Low to high melting point nucleus & Good conductors inner shell e- mobile “sea” of e- Crystal Structures of Metals Type of Crystals And All for the Want of a T < 13 0C Button white tin stable grey tin weak Reference Raymond Chang and Kenneth Goldsby. Chemistry, 12th Edition (2016), Mc-Graw Hill Higher Education, New York, USA.