# Copper - Nickel Example

### By: Vacarro M. Williams

Since my example problem is supposed to be an introduction to the phase diagram, its calculations, and how it is perceived, most of my text is taken from Callister. Caption of the Cu-Ni Phase Diagram figure 9.2 (a)

• (Note: A brief explanation of the caption will be given.)

A good interpretation of a binary phase diagram that is easy to understand and interpret is the Cu-Ni system. This diagram has three different phase regions, the alpha region, the liquid region, and the alpha + liquid region, which are defined by specific compositions and temperatures. The phase boundaries are separated by two lines. The line separating the liquid and the alpha + liquid regions is the liquidous line. The line separating the alpha and the alpha + liquid regions is the solidous line. The intersection of these two lines signify the melting temperatures of the two components individually. The Cu-Ni system is especially noted for its complete liquid and solid solubility of its components, and is thusly identified as an isomorphous system. Caption of the Cu-Ni Phase Diagram figure 9.2 (b)

• (Note: A brief explanation of the caption will be given.)

The determination of phase compositions in a single phase, is just how much of each phase is present at a given temperature. For a double phase region, the procedure intensifies. One has to first draw a horizontal line at the given temperature from the first phase boundary to the second phase boundary. This line is defined as the tie line. Next, at the intersection of each phase boundary with the tie-line, vertical lines are drawn straight down until they intersect the x-axis where the composition of each component is identified.

Through the use of the lever rule, one can also determine the amount of each phase present. The lever rule is an expression which allows one to compute the phase amounts in a two phase alloy equilibrium situation. In a one phase region, the alloy is composed of 100% of that phase. For a two phase region, one has to rely on the combination of the tie line and the lever rule expression. {This paragraph will become more in-depth with time.}

Here, the equations for both the mass fractions of the liquid and alpha phases will be given and discussed.

The process of solidification (cooling) will be discussed here. Caption of the Cu - Ni Phase Diagram figure 9.3

• (Note: This caption can be one of the clickable maps. A brief explanation will also be given after the caption.)

Within the discussion of the solidification process, there will be various hyper linked instructions for the reader, so that a picture will reemphasize what is being stated.

An example (sample) problem will be located here. The example will be similar to example problem 9.2.