A phase diagram is a graphical tool used to illustrate the conditions under which the distinct physical states of a substance, known as phases, are stable. These diagrams map the relationship between variables like pressure, temperature, or concentration, showing where a substance will exist as a solid, liquid, or gas. They represent equilibrium states, meaning the system has reached a stable balance and no net change is occurring. Understanding these charts is fundamental in predicting a material’s behavior under various environmental conditions.
Defining the Diagram’s Elements
The most common phase diagram for a pure substance is a two-dimensional plot, typically using pressure on the vertical axis and temperature on the horizontal axis. These axes define the space of possible conditions under which the substance can exist. Within this space, large areas called regions or fields represent a single, stable phase: solid, liquid, or vapor. A specific combination of temperature and pressure falling into one of these regions means the substance exists entirely in that single state.
Separating these single-phase regions are lines or curves, known as phase boundaries. These boundaries represent the specific conditions where two different phases can coexist in equilibrium. The line separating the solid and liquid regions is the melting or fusion curve. The line between the liquid and vapor regions is the vaporization curve, which shows the boiling point at various pressures. The line between the solid and vapor regions is the sublimation curve, representing the conditions for a direct solid-to-gas transition.
Interpreting Location: Determining the Phase State
Reading a phase diagram involves locating a specific set of conditions and determining the phase or phases present at that point. First, identify the desired temperature value on the horizontal axis and the corresponding pressure value on the vertical axis. The intersection of these two values creates a single point representing the thermodynamic state of the material. If this point falls within one of the labeled regions, the substance exists entirely as the single phase indicated by that region.
When the point of interest lies directly on a boundary line, the substance exists as a mixture of the two phases that the line separates. For example, a point on the vaporization curve signifies that the liquid and gas phases are in equilibrium, such as water boiling at \(100^{\circ}\text{C}\) under atmospheric pressure. If the pressure is increased while keeping the temperature constant, the point moves vertically into the liquid region. Conversely, if the pressure is lowered, the point moves into the vapor region, and the substance is entirely gaseous. This process provides a direct way to visualize the phase changes that occur when either pressure or temperature is altered.
Identifying Critical Equilibrium Points
Phase diagrams contain specific points of fixed conditions that define the limits of phase stability. The most notable is the Triple Point, the single intersection where the three phase boundary lines converge. This point of temperature and pressure is the only condition where the solid, liquid, and gas phases of a pure substance can coexist in stable equilibrium. For water, this occurs at \(0.01^{\circ}\text{C}\) and a pressure of \(0.006\) atmospheres.
Another significant feature is the Critical Point, which marks the upper end of the liquid-gas boundary curve. At and beyond this specific temperature and pressure, the distinction between the liquid and gas phases disappears entirely. The substance transitions into a single, uniform phase known as a supercritical fluid. This fluid exhibits properties between those of a gas and a liquid, possessing the density of a liquid but the flow characteristics of a gas.
Analyzing Composition Changes in Binary Systems
When a phase diagram involves two different components, such as two metals forming an alloy, the diagram typically plots temperature against composition, often fixing the pressure at one atmosphere. These charts, called binary phase diagrams, are used extensively in materials science. In a binary system, regions often exist where the two components are not completely mixed but exist as two separate phases.
To determine the composition of the two phases in such a two-phase region, a tool called a tie line is used. A tie line is a horizontal line, representing a constant temperature, drawn through the two-phase field. This line extends until it intersects the boundary lines on both sides of the two-phase region. The points where the tie line touches the boundaries indicate the specific compositions of the two phases that are in equilibrium at that temperature. For instance, in a liquid-plus-solid region, the intersection on the liquid boundary gives the liquid’s composition, and the intersection on the solid boundary gives the solid’s composition.
Using the Lever Rule
Once the compositions of the two phases are determined using the tie line, the relative amounts (or fractions) of each phase present in the mixture can be calculated using the Lever Rule. This rule is based on the principle of mass balance. The Lever Rule states that the fraction of one phase is proportional to the length of the tie line segment extending from the overall composition point to the boundary of the other phase, divided by the total length of the tie line. The Lever Rule is essential for quantifying the microstructure of materials, allowing prediction of the mechanical properties of alloys.