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Structures of Solids Glass (SiO2) Crystal Solid Noncrystal Crystals • Have an ordered, repeated structure. • The smallest repeating unit in a crystal is a unit cell, which has the symmetry of the entire crystal. • 3-D stacking of unit cells is the crystal lattice. Prentice Hall © 2003 Chapter 11 Basis Crystal structure The basis may be a single atom or molecule, or a small group of atoms, molecules, or ions. Unit cell: 2-D, at least a parallelogram Unit cell is the building block of the crystal : 3-D, at least a parallelepiped (Simple cubic) • Size of the cell • Size of the atoms • Number of atoms in a cell X-ray diffraction Next lecture Count it now! MODEL • Close Packing of Spheres Prentice Hall © 2003 Chapter 11 Most Common Types of Unit Cells based on Close Packing of Spheres Model • Simple Cubic – 1 atom • Body Centered Cubic (BCC) – 2 atoms • Face Centered Cubic (FCC) – 4 atoms Prentice Hall © 2003 Chapter 11 Number of Atoms in a Cubic Unit Cell 1 2 4 Unit Cells Prentice Hall © 2003 Chapter 11 Sample Problem • The simple cubic unit cell of a particular crystalline form of barium is 2.8664 oA on each side. Calculate the density of this form of barium in gm/cm3. Prentice Hall © 2003 Chapter 11 Steps to Solving the Problem • (1.) Determine the # of atoms in the unit cell. • (2.) Convert oA (if given) to cm. (3.) Find volume of cube using Vcube = s3 = cm3 • (4.) Convert a.m.u. to grams. [Note: 1 gm= 6.02 x 1023 a.m.u.] • (5.) Plug in values to the formula: D = mass/volume • Prentice Hall © 2003 Chapter 11 Conversions • Useful Conversions: • 1 nm(nanometer = 1 x 10-7 cm • 1 oA (angstrom)= 1 x 10-8 cm • 1 pm (picometer) = 1 x 10-10 cm • 1 gram = 6.02 x 10 23 a. m. u. (atomic mass unit) Prentice Hall © 2003 Chapter 11 Sample Problem • LiF has a face-centered cubic unit cell (same as NaCl). [F- ion is on the face and corners. Li+ in between.] • • • • Determine: 1. The net number of F- ions in the unit cell. 2. The number of Li+ ions in the unit cell. 3. The density of LiF given that the unit cell is 4.02 oA on an edge. (oA = 1 x 10-8 cm) Prentice Hall © 2003 Chapter 11 Sample Problem • The body-centered unit cell of a particular crystalline form of iron is 2.8664 oA on each side. (a.) Calculate the density of this form of iron in gm/cm3. (b.)Calculate the radius of Fe. • Note: First determine: • A. The net number of iron in the unit cell. • B. 1 oA = 1 x 10-8 cm Prentice Hall © 2003 Chapter 11 The body-centered cubic unit cell of a particular crystalline form of an element is 0.28664 nm on each side. The density of this element is 7.8753 g/cm3. Identify the element.