NATURE OF MATERIALS - Materials for Civil and Construction Engineers - page 69

Soluble Materials The simplest type of phase diagram is for two elements that
are completely soluble in both the liquid and solid phases. Solid solutions
occur when the elements in the alloys remain dispersed throughout the
matrix of the material in the solid state. A two-element or binary phase dia-
gram is shown in Figure 2.14(a) for two completely soluble elements. In this
diagram, temperature is plotted on the vertical axis and the percent weight of
each element is plotted on the horizontal axis. In this case, the top axis is used
for element A and the bottom axis is used for element B. The percentage of
element B increases linearly across the axis, while the percentage of element
A starts at 100% on the left and decreases to 0% on the right. Since this is a
binary phase diagram, the sum of the percentage of elements A and B must
equal 100%. In Figure 2.14(a), there are three areas. The areas at the top and
bottom of the diagram have a single phase of liquid and solid material, respec-
tively. Between the two single-phase areas, there is a two-phase area where the
material is both liquid and solid. The line between the liquid and two-phase
areas is the liquidus , and the line between the two-phase area and the solid
area is the solidus . For a given composition of elements A and B, the liquidus
defines the temperature at which, upon cooling, the first solid crystals form.
The solidus defines the temperature at which all material has crystallized. It
should be noted that, for a pure element, the transition between liquid and
solid occurs at a single temperature. This is indicated on the phase diagram
by the convergence of the liquidus and solidus on the left and right sides of
Figure 2.14(a), where there is pure element A and B, respectively.
A specific composition of elements at a specific temperature is defined
as the state point , as shown in Figure 2.14(b). If the state point is above the
liquidus, all the material is liquid and composition of the liquid is the same
as the total composition of the material. Similarly, if the state point is below
the solidus, all the material is solid and the composition of the solid is the
same as for the material. In the two-phase region between the liquidus and
the solidus, the percent of material that is in either the liquid or solid phase
varies with the temperature. In addition, the composition of the liquid and
solid phases in this region changes with temperature. The compositions of
the liquid and solid can be determined directly from the phase diagram by
using the lever rule. First a tie line is established by connecting the liquidus
and solidus with a horizontal line that passes through the state point, as
shown on Figure 2.14(b). A vertical projection from the intersection of the tie
line and the liquidus defines the composition of the liquid phase. A vertical
projection from the intersection of the tie line and the solidus defines the
composition of the solid phase. For the example in Figure 2.14(b), the alloy
is composed of 50% material A and 50% material B. For the defined state
point, 79% of the liquid material is element A and 21% is element B, and
31% of the solid phase material is element A and 69% of the solid material
is element B. In addition, the percent of the material in the liquid and solid
phases can be determined from the phase diagram. From mass balance, the
total material must equal the sum of the masses of the components; that is,

m t = m l + m s (2.4)