ASM Handbook, Volume 3, Alloy Phase Diagrams Copyright # 2016 ASM InternationalW H. Okamoto, M.E. Schlesinger and E.M. Mueller, editors All rights reserved asminternational.org Introduction to Phase Diagrams* IN MATERIALS SCIENCE, a phase is a a system with varying composition of two com- Nevertheless, phase diagrams are instrumental physically homogeneous state of matter with a ponents. While other extensive and intensive in predicting phase transformations and their given chemical composition and arrangement properties influence the phase structure, materi- resulting microstructures. True equilibrium is, of atoms. The simplest examples are the three als scientists typically hold these properties con- of course, rarely attained by metals and alloys states of matter (solid, liquid, or gas) of a pure stant for practical ease of use and interpretation. in the course of ordinary manufacture and appli- element. The solid, liquid, and gas states of a Phase diagrams are usually constructed with a cation. Rates of heating and cooling are usually pure element obviously have the same chemical constant pressure of one atmosphere. too fast, times of heat treatment too short, and composition, but each phase is obviously distinct Phase diagrams are useful graphical representa- phase changes too sluggish for the ultimate equi- physically due to differences in the bonding and tions that show the phases in equilibrium present librium state to be reached. However, any change arrangement of atoms. in the system at various specified compositions, that does occur must constitute an adjustment Some pure elements (such as iron and tita- temperatures, and pressures. It should be recog- toward equilibrium. Hence, the direction of nium) are also allotropic, which means that the nized that phase diagrams represent equilibrium change can be ascertained from the phase dia- crystal structure of the solid phase changes with conditions for an alloy, which means that very gram, and a wealth of experience is available to temperature and pressure. For example, iron slow heating and cooling rates are used to gener- indicate the probable degree of attainment of undergoes several distinct solid-state changes ate data for their construction. The equilibrium equilibrium under various circumstances. As of its crystal structure with temperature. Alloy- states that are represented on phase diagrams are such, alloy phase diagrams are useful to metal- ing, the formation of a substance with metallic known as heterogeneous equilibria, because they lurgists, materials engineers, and materials properties composed of two or more elements, refer to the coexistence of different states of mat- scientists in four major areas: also affects the occurrence of phase changes. ter (gas, liquid, and/or solid phases with different For example, the temperature for complete melt- crystal structures). When two or more phases are Development of new alloys for specific applications ing (100% liquid phase) of an alloy depends on in mutual equilibrium, each phase must be in the the relative concentration of alloying elements. lowest free-energy state possible under the restric- Fabrication of these alloys into useful configurations Alloying also affects the stable crystalline phase tions imposed by its environment. This equilib- of a solid. Depending on how two or more ele- rium condition means that each phase is in an Design and control of heat treatment proce- ments behave when mixed, the elements may internally homogeneous state with a chemical dures for specific alloys that will produce form different crystalline phases and/or chemical composition that is identical everywhere within the required mechanical, physical, and chemical properties compounds. each phase, and that the molecular and atomic Phase diagrams and the systems they describe species of which the phase is composed (if Solving problems that arise with specific are often classified based on the number of com- more than one) must be present in equilibrium alloys in their performance in commercial ponents (typically elements) in the system proportions. applications (Table 1). A unary phase diagram plots the phase Because industrial practices almost never changes of one element as a function of tempera- approach equilibrium, phase diagrams should ture and pressure. A binary diagram plots the be used with some degree of caution. Kinetic Unary Systems phase changes as a function of temperature for effects, including surface energies, activation energies, and diffusion and reaction rates, affect A system containing only one pure metal is the time needed to initiate and complete a physi- referred to as a unary system, which can exist cal or chemical phase change. With rapid heat- as a solid, liquid, and/or gas, depending on the Table 1 Terminology for the number of ing, any phase change, such as melting, occurs specific combination of temperature and pres- elements in an alloy phase diagram at a slightly higher temperature than with slow sure. Assuming a constant atmospheric pressure, Number of components Name of system or diagram heating. Conversely, with rapid cooling, the a metal melts when heated to a specific tempera- One Unary phase change occurs at a lower temperature than ture and boils with further heating to a specific Two Binary with slow cooling. Therefore, transformations boiling temperature. Through evaporation, metal Three Ternary observed during heating are at higher tempera- atoms leave the container as a vapor. In condi- Four Quarternary Five Quinary tures than the reverse transformations observed tions where matter can enter or leave the system, Six Sexinary during cooling, except in the hypothetical case these systems are known as open systems. Seven Septenary wherein the rates of heating and cooling are infi- To create a closed system where no matter Eight Octanary nitely slow, where the two observations of tem- enters or leaves the system, an airtight cover Nine Nonary Ten Decinary perature would coincide at the equilibrium can be placed on top of the container. If pres- transformation temperature. sure is held constant during boiling, then an * Adapted from F.C. Campbell, Ed., Phase Diagrams: Understanding the Basics, ASM International, 2012, and H. Baker, Alloy Phase Diagrams and Microstructure, Metals Handbook Desk Edition, ASM International, 1998, p 95–114. 4 / Introduction to Alloy Phase Diagrams increase in volume of the closed system must are 14 kinds of space lattices, derived from all the for the “arrest” in temperature during heating or occur. Conversely, if pressure is increased, the possible varieties of interatomic spacing, lattice cooling through the transformation temperature. vapor phase is compressed and the volume of arrangements, and interaxial angles within the The letter A also is followed by the letter c or r the vapor becomes smaller. The volume of liq- seven crystal systems. to indicate transformation by either heating or uid metal remains fairly constant with the appli- cooling, respectively. The use of letter c for cation of pressure; that is, liquid metals are heating is derived from the French word chauf- essentially incompressible. The same situation Polymorphism and Allotropy fant, meaning warming. If cooling conditions holds if the liquid metal is cooled so that only apply, the critical temperature is designated as a solid remains. Metal atoms in a liquid state Some elements and compounds exhibit more “Ar,” with the letter r being derived from the are almost as closely packed as they are in the than one stable solid crystalline phase depen- French word refroidissant for cooling. solid state, so the effects of pressure and vol- dent on temperature and pressure; these materi- Many other metals and nonmetals also exhibit ume change can often be approximated as sta- als are called polymorphic,orallotropic for allotropic transformations (Table 2). For exam- tistically negligible. pure elements. ple, titanium, zirconium, and hafnium all exhibit All pure metals have a unique melting point. The most commonly used allotropic element a transition from an hcp structure to bcc on heat- Metals with weak interatomic bonds melt at is iron, which undergoes a series of phase trans- ing. Note that in each case, a close-packed struc- lower temperatures. This includes several soft formations as a function of temperature and pres- ture is stable at room temperature, while a looser metals such as lead, tin, and bismuth. In contrast, sure (Fig. 3). At room temperature, iron has a bcc packing is stable at elevated temperatures. While the refractory metals have high melting points. structure (also known as ferrite, or a iron). this is not always the case, it is a trend experi- The refractory metals include niobium, tantalum, Ferrite is ferromagnetic at room temperature, enced with many metals. molybdenum, tungsten, and rhenium. A two- but if temperature is slowly increased, a ferrite phase system exists when a container consists becomes paramagnetic at the Curie temperature of both a liquid phase and a vapor phase. In this of 770 C (1418 F). When temperature is increa- Binary Systems example, a liquid is in equilibrium with its vapor sed further, the paramagnetic ferrite changes to phase, when the average rate of atoms leaving an fcc crystal structure referred to as austenite the liquid equals the rate joining the liquid from or g iron. Austenite is completely paramagnetic. A binary phase diagram plots the different the gas. If pressure is increased, the result is At higher temperatures, austenitic iron changes states of matter as a function of temperature for fewer atoms in the gas phase and more in the liq- to a high-temperature bcc structure, referred to a system at constant pressure with varying com- uid phase, and the ratio of atoms in each phase as d iron. Similar phase changes occur during position of two components (or elements). The remains constant once equilibrium (constant cooling. Under equilibrium conditions, the solid- addition of an alloying element represents temperature and pressure) is reestablished. ification of pure iron from the liquid occurs at another degree of freedom (or variable), which 1540 C (2800 F) and forms d iron.