Reading notes Lattice basic and crystal structure is how the crystalline solids are arranged Short range order when atoms go to the next neighbor o Many polymers show SRO Long range order have this crystalline structure in atoms o Most metals alloys semiconductors ceramics some polymers o If it s just one crystalline crystal it s a single crystal used in computer chips o Polycrystalline material is composed of many small crystals with various orientations in space The smaller crystals are known as grains and the boarders between the crystals are known as grain boundaries Amorphous material is the non crystalline one This is most glasses which typically form in ceramic and polymer systems They are gel like materials o The crystallization of these glasses can be controlled They are known as glass ceramics These are quite strong Many plastics are amorphous The unit cell they want a single repeat pattern o There are seven different crystal systems o There are 14 types of lattices Number of atoms per unit cell o In a single cell body there is only 1 atom Because one more is 1 8th of an atom o In a BCC there is 2 atoms o In a FCC there are 8 atoms Atmoic radii and that relates to the lattice Coordinates are important with which way you go too Packing factor atomic packing factor the fraction of space occupied by atoms o Packing factor number of atoms cell volume of each atom volume of unit cell o Equations for volume of unit cell SC BCC FCC one size Density p number of atoms cell atomic mass volume of unit cell Avagadro s Hexagonal close packed structure o Close packed structure ex the packing fraction is the highest possible with atoms of Allotropy pure elements Polymorphism Compounds Miller points How to plot look at book Repeat distance distance between lattice points along the direction Linear density Number of lattice points per unite length along the direction o Also the reciprocal of repeat distance When you construct the direction or plane in the unit cell you work backwards Miller indices are how you write the coordinates Miller bravais indices are used for hexagonal unit cells for the unique symmetry of the system Stacking sequence Anisotropic if the properties depend on the crystallographic direction along which the property is measured Isotropic if the properties are identical in all directions o Most polycrystalline materials will exhibit isotropic properties Interplanar spacing the distance between two adjacent parallel plane of the atoms with the same miller indices Interstitial sites small holes between the usual atoms into which smaller atoms may be placed o It touches two or more atoms in the lattice o Cubic site occurs in the SC o Octahedral sites are in BCC and FCC these have a coordination number of six not eight o Tetrahedral sites are in BCC and FCC these have a coordination number of four Crystal structure of ionic materials o The different ionic material ensure electrical neutrality and allow different sizes of ions o Ionic radii forms anion at the lattice point with the cations then located at the interstitial to be packed efficiently sites o Anions are larger than cations o Electrical neutrality overall material has to be electrically neutral o Anion polyhedra it will share corner o Goes over different types of structures Covalent structures o Diamond cubic structure o Crystalline silica partly covalent and partly inic o Crystalline polymers You can use x ray diffraction to view the crystal structure of a crystalline material