Structures of Solids

Glass (SiO2)

Crystal

Noncrystal

Solid

Prentice Hall © 2003 Chapter 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.

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)

• Number of atoms in a cell

• Size of the cell

• Size of the atoms Next lecture

X-ray diffraction

Count it now!

Prentice Hall © 2003 Chapter 11

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

1 2 4

Number of Atoms in a Cubic Unit Cell

Prentice Hall © 2003 Chapter 11

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

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.