Structures of Solids

Glass (SiO 2 )

Crystal Noncrystal Solid

Prentice Hall © 2003Chapter 11 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.

BasisCrystal 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)

Number of atoms in a cell Size of the cell Size of the atoms Next lecture X-ray diffraction Count it now!

Prentice Hall © 2003Chapter 11 MODEL Close Packing of Spheres

Prentice Hall © 2003Chapter 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

124 Number of Atoms in a Cubic Unit Cell

Prentice Hall © 2003Chapter 11 Unit Cells

Prentice Hall © 2003Chapter 11 Sample Problem The simple cubic unit cell of a particular crystalline form of barium is o A on each side. Calculate the density of this form of barium in gm/cm 3.

Prentice Hall © 2003Chapter 11 Steps to Solving the Problem (1.) Determine the # of atoms in the unit cell. (2.) Convert o A (if given) to cm. (3.) Find volume of cube using V cube = s 3 = cm 3 (4.) Convert a.m.u. to grams. [Note: 1 gm= 6.02 x a.m.u.] (5.) Plug in values to the formula: D = mass/volume

Prentice Hall © 2003Chapter 11 Conversions Useful Conversions: 1 nm(nanometer = 1 x cm 1 o A (angstrom)= 1 x cm 1 pm (picometer) = 1 x cm 1 gram = 6.02 x a. m. u. (atomic mass unit)

Prentice Hall © 2003Chapter 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 o A on an edge. ( o A = 1 x cm)

Prentice Hall © 2003Chapter 11 Sample Problem The body-centered unit cell of a particular crystalline form of iron is o A on each side. (a.) Calculate the density of this form of iron in gm/cm 3. (b.)Calculate the radius of Fe. Note: First determine: A. The net number of iron in the unit cell. B. 1 o A = 1 x cm

The body-centered cubic unit cell of a particular crystalline form of an element is nm on each side. The density of this element is g/cm 3. Identify the element.