Crystallography

● Short-Range Order - refers to the special arrangement of atoms that extends only to the atom’s nearest neighbors ● Long-Range Order - refers to the special atomic arrangement that extends over length scales of 10 nanometers ● Crystalline Solid - a material in which the atoms are arranged in a repeating or periodic array over large atomic distances ● Amorphous Solid - exhibits only a short-range order of atoms or ions ● Glass - typically forms in ceramic and polymer systems ● Plastic - is composed of relatively large chains of polymer molecules that get entangled with each other ● Atomic Hard-Sphere Model - atoms are thought of as being solid spheres representing nearest neighbor atoms touching one another ● Unit Mesh - a collection of plane lattices ● Primitive (p) Unit Mesh - lattice nodes occur only at their corners ● Centered (c) Unit Mesh - lattice nodes occur at the center ● Lattice Node - refers to a point in a unit mesh that represents one particle ● Plane Lattice - refers to the collection of lattice points ● Unit Cell - refers to the basic structural unit of a crystalline solid that represents crystal symmetry of a crystal structure ● Lattice Parameters - refers to the axial lengths or dimensions of the unit cell ● Bravais Lattices - refers to the unique three-dimensional arrangements of lattice points named after Auguste Bravais ● Simple Cubic Structure (Primitive Lattice) - a0=2r, where a0 is the side length and r is the atomic radius ● Body-Centered Structure - a0 = 4r/sqrt(3) ● Face-Centered Structure - a0 = 4r/sqrt(2) ● Hexagonal Close-Packed Structure - c0 /a0 = sqrt(8/3) = 1.633 ● Coordination Number - refers to the number of atoms touching a particular atom or the number of nearest neighbors ● Atomic Packing Factor - refers to the fraction or space occupied by atoms. ● Density - mass over volume ● X-ray Diffraction - refers to the scattering of X-rays by the units of a crystalline solid ● Max von Laue - recommended that since the wavelength of X-rays is comparable in magnitude to the distances between lattice points in a crystal, the lattice should be able to diffract X-rays ● Interference - produce an X-ray diffraction pattern ● Constructive Interference ● Destructive Interference ● Scattering of X-rays - the process by which a beam of X-rays is directed at a mounted crystal and atoms in the crystal absorb some of the incoming radiation and then reemit it ● Bragg’s Law - determines the angles of coherent and incoherent scattering from a crystal lattice ● Electron-Density Contour Map - tells the relative electron densities at various locations in a molecule ● Ionic Crystals - composed of charged species, and have high melting points. It is not a conductor of electricity when in solid state but in a liquid. ● Lattice Energy - the higher the lattice energy, the more stable the compound. ● Covalent Crystals - exist when atoms are held together in an extensive three-dimensional network altogether by covalent bonds. ● Allotropy - refers to the arrangement of atoms in a crystal structure based on temperature and pressure. ● Diamond - each carbon is tetrahedrally bonded to four other carbon atoms and it has a melting point of 3550 degrees Celcius. ● Graphite - a good conductor of electricity in directions along the planes of carbon atoms ● Quartz (SiO2 ) - has a similar arrangement to that of carbon in diamond. Similar to diamond in many aspects because of its hardness and melting point of 1610 degrees Celcius. ● Molecular Crystals - the lattice points are occupied by molecules that have Van der Waals forces and/or hydrogen bonding ● Van der Waals Forces - refers to a general term used to define the attraction of intermolecular forces between molecules ● Weak London Dispersion Forces - Instantaneous Dipole ● Dipole-Dipole Forces - occur in molecules that are permanently polar ● Molecular Crystals - the molecules are packed together as closely as their size and shape allow. Most molecular crystals melt at temperatures below 100 degrees Celcius. ● Metallic Crystals - have the simplest structure because every lattice point in the crystal is occupied by an atom of the same metal ● Amorphous Solids - lack a regular three-dimensional arrangement of atoms ● Glass - an optically transparent fusion product of inorganic materials that has cooled to a rigid state without crystallizing ● Silicon Dioxide - the chief component of glass ● Color of the Glass - because of the presence of metal ions as oxides - impurities. ● Green Glass - contains Fe2O3 or CuO ● Yellow Glass - contains UO2 ● Blue Glass - CoO and CuO ● Red Glass - contains small particles of gold and copper ● Symmetry Operation - operation performed on an object which leaves it in a configuration that is indistinguishable from and superimposable on the original configuration ● Symmetry Element - refers to the symmetry operation that is carried out with respect to points, lines, or planes.