Читать книгу Engineering Physics of High-Temperature Materials - Nirmal K. Sinha - Страница 50

A material system is composed of both phases and components. “Phases (P)” in a system are homogeneous in chemical composition and physical state. “Components (C)” in a system represent a pure element or compound. The number of components in a system is thus the number of independent species necessary to define the composition of all the phases. Phase diagrams map the preferred or equilibrium phases of a material at different thermodynamic variables.

For a single‐component system, a simple pressure–temperature phase diagram is a useful tool to understand the phase boundaries of the material. Figure 2.3 shows the typical features of such a phase diagram. The lines on the graph map the phase boundaries that exist at equilibrium. The open spaces between the lines represent areas where a single phase exists. Phase transitions occur on the lines. These phase transitions can occur due to a change in temperature or pressure and sometimes different terminology is used to indicate that a specific parameter is changing. For example, “melting”/“freezing” are generally terms used for liquefaction/solidification phase transitions between solid and liquid due to a change in temperature.

The degrees of freedom, F, is the number of thermodynamic parameters that may vary independently while maintaining the same phase/phases. F can be derived from the number of components (C) and phases (P), according to the phase rule (Gibbs 1874–1878 ):

(2.1)

For the simple one‐component system being considered, in each single‐phase region C = 1 and P = 1 such that F = 2. Two parameters (temperature and pressure) can thus be chosen independently within this region. However, on the lines of the phase diagram, P = 2 and F = 1, and selection of one parameter influences the other. For example, on the curve between liquid and gas, if the temperature decreases, some of the gas condenses, decreasing the pressure. When three phases coexist in a single‐component system, F = 0 suggesting that this can only occur at a single temperature and pressure. This point is known as the “triple point.”

Figure 2.3 Typical pressure versus temperature of a one‐component system. T _TP and P _TP represent the triple point temperature and pressure, respectively, while T _C and P _C represent the critical temperature and pressure, respectively. Phase transitions are represented in gray and are not shown on a real phase diagram.

Another key point on such phase diagrams is the end point of a phase equilibrium curve – called a “critical point.” Figure 2.3 demonstrates a common critical point where the liquid and gaseous states become indistinguishable and are often referred to as a supercritical fluid. In the vicinity of a critical point, the physical properties of the liquid and vapor can dramatically change as they become more similar. Historically, a solid–liquid critical point has generally not been accepted (Landau and Lifshitz 1980); however, this has recently been challenged – largely through molecular dynamics simulations (Elenius and Dzugutov 2009; Mochizuki and Koga 2015).

It should be mentioned that the phase diagram of a single compound is not necessarily a single‐component system. Polymorphism can give rise to intricate phase diagrams for single compounds. For example, the phase diagram of water is quite complex and discussed further in Section 2.6.

Phase diagrams for mixtures of chemically independent components can quickly become increasingly complex. For a simple binary mixture, the open spaces in a pressure–temperature phase diagram would have C = 2 and P = 1 to give three degrees of freedom. The third degree of freedom is the composition of one of the two components. For this reason, phase diagrams for binary systems are generally expressed as temperature versus composition at a given pressure (often standard pressure), as shown in Figure 2.4. Engineers will often express the composition in terms of the weight percent of the components while chemists will often express it in terms of the mole fraction of the component.

Figure 2.4 Sample phase diagram schematic for a binary XY system. (a) Simple phase diagram demonstrating how to determine the composition present in the different phases at a point in the mixed phase region. (b) Slightly more complex phase diagram of an XY system containing a eutectic point.

Phase diagrams for binary systems contain a large amount of information. Not only do they give an indication of the phases present, but also provide information about the composition of the phases and fraction of the phases present in the mixture. For example, the point of interest highlighted in Figure 2.4a has both a liquid phase and a solid phase present. The composition of the phases can be determined by drawing a tie‐line from the point to the liquidus and solidus curves and then reading the percent composition at the intersections. The ratio of the liquid/solid present can then be determined using the two phase compositions and the overall composition, using the lever rule:

(2.2)

Figure 2.4b presents a typical phase diagram of a eutectic system. A eutectic system is a homogeneous mixture of substances that melts or solidifies at a single temperature that is lower than the melting point of any of the constituents. At a eutectic point, the liquid and two solid solutions all coexist in chemical equilibrium. Cooling through this temperature results in intricate macrostructures that can take several different forms, including lamellar, rod‐like, globular, or acicular (needle‐like) structures. Other critical points in a binary system include:

 Eutectoid: Transformation of a solid phase to yield two solid phases.

 Peritectic: Transformation of a liquid phase and a solid phase to yield a single solid phase.

 Peritectoid: Transformation of two solid phases in an alloy system to yield a new solid phase.

Binary systems can be intricate with multiple types of transformations available to the system at different compositions. Further increasing the number of components can quickly make materials' systems very complex. Phase diagrams can thus be incredibly useful in designing materials to have specific phase compositions.

Phase diagrams can be incredibly important in engineering materials, but they do not always tell the whole story. Phase diagrams generally present equilibrium phases. Nonequilibrium phases, such as phases stabilized through quenching or even a more complex environmental history, can often be critical to achieving properties of interest. Time–temperature–transformation diagrams that plot the time required for isothermal transformation provide kinetic information about transformation processes and can be highly useful in developing synthesis processes; however, these diagrams must still be interpreted with the assistance of phase diagrams.