Phase Diagrams

Type of physical science: Phase Diagrams, Gases; behavior of, Pressure, Temperature, Solids, Liquids, Chemistry

Field of study: Chemical methods

Phase diagrams represent a graphical presentation of the relationship between the number, quantity, and composition of various phases present in a system consisting of one or more components and the composition, pressure, and temperature of the system. Typical phase diagrams are presented as variations in two of the independent parameters when the third parameter of the system is constant.

Overview

Phase diagrams are graphical plots that are based on experimental and mathematical analysis and that express the physical conditions under which various solid, liquid, and vapor phases can exist in equilibrium for a single or multicomponent system. For a pure substance, a phase diagram is simply a graphical representation of the pressure plotted against the temperature; such a diagram can be used to identify the combination of pressure and temperature under which the substance exists as a solid, liquid, or vapor and in what circumstances it will undergo phase change from solid to liquid, solid to vapor, or liquid to vapor. In order to address various possible phase changes, the phase diagram of a pure substance consists of a melting-point line, a vapor-pressure line, a sublimation-pressure line, a critical point, and a triple point. The nature and types of phase diagrams that are applicable to mixtures of two or more components depend on the composition of the mixture. The phase diagram of a mixture consisting of two or more components is much more complex than the phase diagram of a pure substance. A single pressure-versus-temperature plot is usually unable to describe the complete phase behavior of such a system. A system consisting of a mixture of different substances can exhibit a gaseous phase, one or more liquid phases, and one or more solid phases. Each phase is separated from other phases by a boundary but need not be continuous. These phases are different from one another in their physical properties, a fact that is used to distinguish between different phases. For example, the density and refractive index of two liquid phases in an oil-water system are different. As a result, the oil phase floats on top of the water phase as a result of its lower density and is visibly distinguishable from water because of the differences in the refractive index.

The phase diagram of a pure substance consists in part of a melting-point line, which represents the solid-phase/liquid-phase equilibrium conditions. The melting-point line allows a determination of the temperature at which the substance transforms from a solid to a liquid and vice-versa as a function of pressure. A substance can exist only as a solid at temperatures below the melting point, and only as a liquid at temperatures above the melting point. Usually, the melting-point temperature of a substance changes as the pressure is increased. For example, the melting-point temperature of ice decreases when the pressure is increased. Therefore, when two blocks of ice are pressed together, localized melting takes place at the point of contact; when the pressure is released, the liquid again freezes, causing the two blocks to weld into a single block.

The melting-point line intersects the boiling-point or vapor-pressure line at the "triple point." This is a pressure-temperature combination at which the solid, the liquid, and the vapor phase can coexist simultaneously. For a pure substance, there is only one combination of pressure and temperature values at which the three phases can exist simultaneously.

The curve representing the equilibrium between a solid and a vapor phase, and direct transformation of a solid to a vapor phase, is referred to as the "sublimation curve." For a solid substance at constant pressure, as the temperature is raised to intersect the sublimation curve, the substance completely vaporizes before its temperature can rise further. A substance exhibiting sublimation is solid carbon dioxide, commonly referred to as "dry ice," which evaporates into a gaseous state at atmospheric conditions.

The curve representing the equilibrium conditions between the liquid and the vapor phase is referred to as the "boiling-point line" or "vapor-pressure line." At the selected pressure conditions, a pure substance can exist only as a liquid at temperature values lower than the boiling-point temperature and only as vapor or gas at temperature values higher than the boiling-point pressure. As the pressure of the system increases, the boiling-point temperature usually increases. At a certain pressure level referred to as the "critical pressure," however, the vapor-pressure curve is terminated, and increasing the temperature does not lead to a phase change. In a physical sense, this means that at pressures equal to or higher than the critical pressure, the concept of the boiling point is not applicable, and as the temperature is increased, the properties of the substance undergo gradual change without a step change. The concept of a critical point can be explained by observing that as one moves along the boiling-point curve from the triple point to the critical point, the properties of the equilibrium liquid and gas phases gradually become similar, and at critical point, they become identical. Since the detection of phase change, from liquid to vapor, depends upon a step change in physical properties, such as density and refractive index, no phase change is detected above the critical point; when pressure and temperature change above the critical point, the properties of a fluid change without the occurrence of a step change. For example, in the fluid pairs air-water, steam-water, nitrogen-water, and methane-oil, the gaseous fluid has much lower density than the liquid. As one moves from one fluid to the other, a step change in the density and other fluid properties is observed at the boundary of the fluid pair. Such step change in refractive index of the fluid at the boundary makes it possible to detect the boundary, which is often referred to as the "interface." As the pressure increases, the properties of the two fluids in the pair become more similar; as a result, a larger number of molecules of each fluid in the pair can dissolve in the other fluid. This is especially true for gas-liquid interfaces. At some very high pressure, referred to as the "critical pressure," all properties of the two fluids in the pair are identical, and all molecules of one fluid can readily dissolve into the other fluid, resulting in only one fluid. At this pressure, by definition, there is only one fluid in the system, and the boundary disappears. The two fluids at pressure above the critical pressure are referred to as "completely miscible," and the mixture of the two fluids is referred to as a "supercritical" fluid.

An important feature of pure-substance phase diagrams is that for a given temperature, two phases can coexist in equilibrium only at one pressure, and three phases can coexist only at one combination of pressure and temperature referred to as the "triple point." This behavior is a manifestation of the phase rule, a mathematical formulation that relates the number of independent characteristics (or the "degrees of freedom") to the number of phases, the number of components, and the number of independent properties. Applying phase rule to a system with two or more components shows that two phases can exist in equilibrium over a range of pressures for a fixed temperature value. The properties of a multicomponent system depend not only on pressure and temperature but also on composition. For a two-component system, one additional parameter is thus added; therefore, the phase diagram of a binary system can be completely represented in a three-dimensional space. For a three-component system, a phase diagram at a fixed pressure and temperature is represented as a ternary, or triangular, diagram. In a ternary phase diagram, the three components are located at three vertices of a triangle, and various locations on the triangle represent mixtures with varying compositions. For systems with more than three components, accounting for individual components in the system becomes almost impossible, and emphasis is usually placed upon the variations of the amounts of the various phases with pressure, temperature, and concentration of a key component.

Phase diagrams are not restricted to systems exhibiting solid-liquid and liquid-vapor pairs. Many practical systems involve multiple solid phases, as in metallic alloys, ceramics, and polymers. Phase diagrams for alloys describe the pressure, temperature, and composition conditions for which the crystal structure or grain structure re-arranges to achieve a different arrangement, giving rise to a different solid phase. Such phase changes from one solid to another with changes in lattice and grain structure are usually not accompanied by significant density changes. However, the mechanical properties of different solid phases of an alloy can be dramatically different. Solid-solid phase changes are also applicable to polymer systems and are described by corresponding phase diagrams.

Phase diagrams for multiple liquid phases are also very useful. Such liquid phases can coexist without dissolving in one another because of differences in the nature of molecules. Below the critical pressure, the two or more liquids in the system can be distinguished by the presence of a visible, definable boundary, or interface, and are referred to as "immiscible" fluids. Two liquids are usually immiscible because of significant differences in their molecular composition. For example, water and most oils are immiscible because water molecules are polar and oil molecules are usually nonpolar. Water and alcohols of lower molecular weights are miscible because the polar character of smaller alcohol molecules controls their behavior. On the other hand, water is not miscible with alcohols of larger molecular weights, because in such alcohols, a long chain of covalently bonded organic molecules controls their behavior. For liquid-liquid systems, the density contrast is usually not as significant as it is for the gas-liquid systems. A more important characteristic for a liquid-liquid system is the nature of bonding in the molecules of the two liquids in the pair. For example, for many oil-water systems, the density contrast is not very large, but oil and water are very different because of the nature of bonding in oil and water molecules, respectively. Water molecules are held together by ionic bonds, causing them to be very polar. On the other hand, molecules in most oils are held together by covalent bonds, causing the oil molecules to be nonpolar. Usually, the polar liquids do not mix with nonpolar liquids, resulting in a boundary with an interfacial tension. The phase diagrams of such systems typically illustrate the effect of solvent concentration on the extent to which two liquids can dissolve in each other.

Applications

Phase diagrams offer an easy-to-use and practical tool that incorporates the theoretical and empirical understanding of the behavior of a multiphase system. Phase diagrams allow a better understanding and representation of the physical properties of various solid, liquid, and vapor phases that may simultaneously exist. Phase diagrams are important to the efficient and economical separation and purification of the components of many natural and synthetic raw materials such as petroleum, coal tar, raw sugar, and alcohols.

Phase diagrams are used to represent and understand the behavior of multiple-component, multiphase systems encountered in a wide spectrum of applications affecting day-to-day life. Broad areas in which phase diagrams are important include metallurgy, materials science, electronics, glass technology, battery technology, ceramics, refrigeration, and power generation. In addition, phase diagrams find important applications in the geosciences for understanding igneous and metamorphic rocks, stratigraphy, and petroleum geochemistry.

Phase diagrams are of great benefit in understanding the volumetric behavior of gas and oil mixtures in subsurface reservoirs, during the transport from the reservoirs to the surface, in surface separation and processing, during transport to refineries, and in the distillation and refining process. A clear understanding of the phase diagrams of oil-gas systems is essential for predicting the future performance of a subsurface reservoir and for designing surface facilities, pipelines, and refineries.

An important manifestation of phase behavior and application of phase diagrams relates to water. The phenomena of cloud formations, rainfall, hailstorms, and snowfall are all related to the phase behavior of water in one of the three possible forms, solid, liquid, or vapor. The phase diagram of water thus has global implications; such phenomena as the melting of snow and the existence of polar ice caps and glaciers are all controlled by the melting-point line on this diagram. Conditions under which water in lakes and oceans evaporates, becomes visible as clouds or fog, and finally condenses in the form of raindrops are easily understood in the context of the vapor-pressure line or the boiling-point line on the phase diagram. The phase diagram of water also finds application in the operation of thermal power plants, which use heat contained in a fuel to convert water to steam that, in turn, drives the turbines for power generation.

The applications involving refrigeration and air-conditioning are developed based on the unique characteristics of the phase diagrams of chemicals referred to as "refrigerants." In such applications, a liquid refrigerant picks up excess heat from the space to be cooled and uses it for its transformation into the vapor phase. The vapor is then cooled by rejecting heat to the atmosphere after it has been compressed to a higher pressure.

Phase diagrams are important in metallurgy for understanding the behavior of and developing metallic alloys, which are used in a wide range of applications. Phase diagrams are useful in the manufacturing and processing of metallic alloys, ranging from various commonly used steels to the most exotic titanium alloys. The ability of engineers to shape solid metals into a variety of useful shapes depends directly upon the phase changes encountered by mixtures of metals when their temperature level is changed. Thus, most steels when heated to a specified temperature go through a phase change, as a result of which the crystalline structure of constituent molecules changes, leading to a new solid phase that is softer and easier to deform. Steels, when heated to this temperature, can be worked readily into many useful objects, and the strength of steel can be recovered simply by cooling the objects.

Another interesting characteristic of alloys, as revealed by their phase diagrams, is that the final properties of an alloy depend upon the heat cycle to which it has been subjected. For example, a rapid cooling of steels from high temperatures, referred to as "quenching," leads to fine-grained, harder, more brittle objects, which are useful in making cutting tools. On the other hand, a gradual cooling from high temperature leads to coarse-grained, softer objects. Such unique characteristics of metal alloys, revealed by phase diagrams, have allowed the manufacture of useful objects with widely varying physical characteristics from the same basic raw material.

Phase diagrams of ceramic materials are the key to obtaining fine china, coffee mugs, dinnerware, and a whole range of other ceramic items used in day-to-day life. A clear understanding of the temperatures at which the clay items must be processed in order to obtain ceramics with desired characteristics is obtained from the phase diagrams of the ceramic and glazing materials.

Phase diagrams of water-oil-detergent-soap systems are critical for the design of effective cleaning systems for laundry, household, and industrial use. Such systems involve phase equilibriums between water and oil, which are usually immiscible. The addition of a detergent to water allows it to dissolve oil, setting the dirt free from the surfaces to be cleaned. Phase diagrams reveal the concentration of detergent that provides optimum dissolution of oil in water under specified temperature conditions.

Context

The critical phenomena of liquids have fascinated physical chemists for more than a century. These phenomena was first observed by Cagniard de la Tour in 1822. The research of this topic under controlled conditions was spurred about fifty years later by the work of Andrews and Van der Waals in the 1870's. All the thermodynamic equilibrium and stability conditions needed in the calculation of phase equilibriums were derived by J. Willard Gibbs from 1870 to 1880. In the same decade, van der Waals proposed his famous theory for determining long-range attractive forces between molecules. Gibbs derived the phase rule, which forms the basis of obtaining phase diagrams, in 1875. According to the phase rule, a system of one component and two phases has one degree of freedom--that is, either its pressure or temperature may be changed--but there is a unique relationship between pressure and temperature for liquid-vapor or solid-vapor equilibrium.

Phase diagrams are found in natural and synthetic systems that surround all forms of matter and affect virtually every aspect of living and physical systems. Advances in the understanding and applications of phase behavior, expressed as phase diagrams, cross the disciplinary boundaries and have truly matured into a rigorous discipline that unifies the principles of physics, chemistry, mathematics, and materials science. Phase diagrams for metals, ceramics, and plastics have facilitated the invention and manufacture of innovative alloys that have contributed to the miracles of engineering witnessed in the twentieth century. Phase diagrams of hydrocarbon systems have allowed the refining of gasoline, aviation kerosene, and other fuel and energy resources that have fueled the transportation industry and other industrial developments. As the frontiers of science are pushed further, an enhanced understanding of phase diagrams will no doubt continue to facilitate the process of finding solutions to new sets of challenging problems.

Principal terms

COMPONENT: An identifiable and separable constituent molecule type in a system consisting of a mixture of various types of molecules

EQUATION OF STATE: A relationship between the pressure, volume, and temperature of a system and the composition of volume fractions of various phases present in the system

INTERMOLECULAR FORCES: Forces exerted by molecules on other molecules; they can be attractive or repulsive depending on the nature of molecules and their distance of separation

PHASE: A homogeneous and physically distinguishable region of a system that is separated from other regions of the system by an interface and differs from other phases in system in its physical and chemical properties

STEP CHANGE: A change in a substance's physical properties, such as density and refractive index, that indicates the occurrence of a phase change

Bibliography

Ahmed, Tarek. Hydrocarbon Phase Behavior. Houston, Tex.: Gulf Publishing, 1989. Describes the fundamentals of phase behavior and phase diagrams for hydrocarbon systems and their applications in reservoir and production engineering. Excellent presentation of theory, applications, solved examples and exercises, as well as numerous illustrations, tables, references, and subject index.

Gibbs, Willard J. The Collected Works of J. Willard Gibbs. Reprint. New Haven, Conn.: Yale University Press, 1948. This collection offers readers an insight into the mind of a great scientist who did some of the original work on phase behavior and phase diagrams. Difficult but worthwhile.

Israelachvili, Jacob N. Intermolecular and Surface Forces. San Diego, Calif.: Harcourt Brace Jovanovich, 1992. Presents both a historical and a modern view of the intermolecular and other forces that govern phase diagrams. Includes discussion of fundamental concepts as well as more dvanced analysis of intermolecular forces. Assumes a basic knowledge of physics, chemistry, and mathematics. Excellent illustrations, references, clear explanations and examples, references, and index.

Lake, Larry W. Enhanced Oil Recovery. Englewood Cliffs, N.J.: Prentice-Hall, 1989. Presents a comprehensive treatment of the applications of phase diagrams in improving oil and gas recovery from subsurface reservoirs. Provides a clear look at the use of phase diagrams in mobilizing oil trapped in the interstices of porous rocks. Excellent presentation of applications; illustrations, references, author and subject index.

Marsh, J. S. Principles of Phase Diagrams. New York: McGraw-Hill, 1935. A classic book that focuses on the fundamental descriptions of phase diagrams in metallurgy, using illustrations. References, subject index.

Rhines, Frederick, N. Phase Diagrams in Metallurgy: Their Development and Application. New York: McGraw-Hill, 1956. A classic book that provides invaluable insight into the bewildering range of applications of phase diagrams to metallurgy. The author has utilized superb illustrations to assist in the understanding of multi-component phase diagrams. Illustrated examples, practice exercises, references, and subject index.

Van Oss, Carol J. Interfacial Forces in Aqueous Media. New York: Marcel Dekker, 1994. Includes treatment of surface, solution chemistry, and phase behavior of solutions and interfaces. Bibliographical reference and index.