The lever rule is a tool used to determine weight percentages of each phase of a binary

Binary

- Mathematics :* Binary numeral system, a representation for numbers using only two digits * Binary function, a function in mathematics that takes two arguments- Computing :* Binary file, composed of something other than human-readable text...

 equilibrium phase diagram

Phase diagram

A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium...

. It is used to determine the percent weight of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus

Solidus

Solidus may refer to:*Solidus , the "⁄" grammatical punctuation character, also used in mathematics*Slash a sign, "/" used as a punctuation mark and for various other purposes...

.

Binary Phase Diagrams

Before any calculations can be made a tie line is drawn on the phase diagram to determine the percent weight of each element; on the phase diagram to the right it is line segment

Line segment

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment...

LS. This tie line is drawn horizontally at the composition's temperature from one phase to another (here the liquid to the solids). The percent weight of element B at the liquidus is given by w_l and the percent weight of element B at the solidus is given by w_s. The percent weight of solid and liquid can then be calculated using the following lever rule equations:



where w_o is the percent weight of element B for the given composition.

The numerator of each equation is the original composition we are interested in +/- the Opposite lever arm. That is if you want the percent weight of solid then take the difference between the liquid composition and the original composition. And then the denominator is the overall length of the arm so the difference between the solid and liquid compositions.

Eutectic Phase Diagrams

There is now more than one, two phase region. The tie line drawn is from the solid alpha to the liquid and by dropping a vertical line down at these points the wt% of each phase is directly read off the graph, that is the percentage weight of the x axis element. The same equations can be used to find the total percentage of alloy in each of the phases, i.e Xs is the percentage of the whole sample in the liquid phase.