Chemistry 103A; Sections 5, 6, 7, 8; Lecture 38, 27 Nov 00

We were talking about:

Phase Diagrams

Recall that phase diagram is p vs T graph which summarizes a great deal of information on the properties of substances. On a phase diagram the space is divided into regions according to the state of the substance at each pressure and temperature. A typical phase diagram might look like:


A point where three phase lines meet is called a "triple point" because at this point, and only at a triple point, the three phases, in this case solid, liquid, and gas, can exist all at the same time in equilibrium with each other.

(Many substances, water and sulfur for example, have more than one solid phase. When this occurs there will be more than one triple point. A "quadruple point," that is, a point where four phases are in equilibrium at the same temperature and pressure is impossible.) You will notice that on our phase diagram the temperature of the triple point is lower than the melting point. This is the usual case. However, for water the triple point is 273.16 K and the melting point is 273.15 K. The phase diagram for water would look qualitatively different, like,


The negative slope of the solid/liquid line has an enormous impact on life on our planet. (I have exaggerated the negative slope on this diagram. On this scale it would look like the line went straight up.)

You are probably aware that solid CO2 does not melt at one atmosphere pressure. The phase diagram for CO2 would look something like,

Crossing a line requires a gain or loss of energy. Crossing the line from solid to liquid requires that the system absorb energy, which we called DHfus, and crossing from liquid to gas requires an energy which we called DHvap. (chapter 6)

The slopes of the lines on a phase diagram can be related to the DH of the phase transition involved. One example, called the Clausius-Clapeyron equation is given in your text on page 604.
 
 

Solids

There are five classes of solid substances. The classes are

Ionic                             NaCl, CaCl2

Metallic                        Ag, Au, Fe

Molecular                     H2O, N2, I2

Network                       diamond, graphite, SiO2

Amorphous                   glass, many plastics


In the first four of these the structure of the solid is a regular array of ions, molecules, or atoms called a crystal. Crystals have "long range order." That is, the detailed structure repeats over and over again over long distances in the crystal.

Crystalline solids have well-defined melting points. That is, the material remains a solid on heating until the melting point is reached and then will remain at the melting temperature until enough heat has been absorbed to melt the entire sample. Amorphous (which means "formless") solids do not have long range order. The molecules are jumbled together almost at random so that there is no regularity or repetition of their arrangement. Amorphous solids do not have well defined melting points. If you heat an amorphous solid it will gradually soften. If you keep heating it the material will continue to soften until it becomes a viscous liquid. There is no temperature where you can say that the material is a solid below that temperature and a liquid above it.

We will not say much more about amorphous solids in this course.
 
 

 Crystal Lattices

"Crystal lattice" is the name given to the structure of a crystalline solid. If you think of the atoms in a crystalline solid as points then these points would form an array called a lattice. Drawing lines between adjacent atoms would produce a three-dimensional grid with a repeating structure.

There are seven basic crystal lattice systems. These seven basic crystal systems are described on p 612 of your text.

We will show graphics of some of these systems

Cubic

Tetragonal

Orthorhombic


Cubic Systems

There are three types of cubic crystals

Simple cubic

Body-centered cubic

Face-centered cubic


Unit Cells

The unit cell is the smallest geometric unit whose repetition (by translation, but without rotation) will create the crystal.

We will describe a number of unit cells in class.
 

Counting Atoms in a Unit Cell

When we count the number of atoms in a unit cell we count only the parts of atoms that are entirely within the unit cell.

Atoms entirely within the unit cell (such as the center of a bcc cell) count as one atom.

Atoms centered in the face of a unit cell (such as the faces in an fcc cell) count as one-half atom.

Atoms at the corners of a cubic, tetragonal, or orthorhombic cell count as one-eighth of an atom.

 Dimensions of Atoms

We can use the dimensions of a unit cell to calculate the diameters of atoms.