Phase Diagram

12 Key excerpts on "Phase Diagram"

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  Advances in Chemical Engineering

  • Zeeshan Nawaz, Shahid Naveed, Zeeshan Nawaz, Shahid Naveed(Authors)
  • 2012(Publication Date)
  • IntechOpen

    (Publisher)

  Part 4 Separation Technology 19 Phase Diagrams in Chemical Engineering: Application to Distillation and Solvent Extraction Christophe Coquelet 1,2 and Deresh Ramjugernath 1 1 Thermodynamic Research Unit, School of Chemical Engineering, University KwaZulu Natal, Howard College Campus, Durban 2 MINES ParisTech, CEP/TEP - Centre Énergétique et Procédés, Fontainebleau 1 South Africa 2 France 1. Introduction By definition, a Phase Diagram in physical chemistry and chemical engineering is a graphical representation showing distinct phases which are in thermodynamic equilibrium. Since these equilibrium relationships are dependent on the pressure, temperature, and composition of the system, a Phase Diagram provides a graphical visualization of the effects of these system variables on the equilbrium behavior between the phases. Phase Diagrams are essential in the understanding and development of separation processes, especially in the choice and design of separation unit operations, e.g. knowledge about high pressure phase equilibria is essential not just in chemical processes and separation operations, but is also important for the simulation of petroleum reservoirs, the transportation of petroleum fluids, as well as in the refrigeration industry. In order to utilize the knowledge of phase behavior it is important to represent or correlate the phase information via the most accurate thermodynamic models. Thermodynamic models enable a mathematical representation of the Phase Diagram which ensures comprehensive and reproducible production of Phase Diagrams. The measurement of phase equilibrium data is necessary to develop and refine thermodynamic models, as well as to adjust them by fitting or correlating their parameters to experimental data. Generally the measurement of phase equilibria is undertaken using two categories of experimental techniques, viz.

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  Principles of Inorganic Materials Design

  • John N. Lalena, David A. Cleary, Olivier B.M. Hardouin Duparc(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  11 Phase Equilibria, Phase Diagrams, and Phase Modeling

  Phase Diagrams, phase equilibria data in graphical form, are a standard tool of materials scientists and engineers. Such compilations of data can be indispensable when, for example, there are questions about the thermodynamic stability of a phase under a given set of working conditions, or in a particular operating environment (e.g. materials compatibility issues). The easiest way for a metallurgical engineer to determine whether an aluminum or tungsten vessel would be the best choice as a container for molten zinc is to consult the Al–Zn and W–Zn Phase Diagrams. In this particular case, the Phase Diagrams would show that Al–Zn alloy formation would be expected to occur since zinc exhibits an increasing solid solubility in aluminum with temperature, whereas tungsten is much more resistant to corrosion by molten zinc.

  The solid‐state chemist interested in preparing new materials also finds Phase Diagrams valuable. Strictly speaking, Phase Diagrams describe the phase relationships within single‐component or multicomponent systems in stable thermodynamic equilibrium. Hence, the Phase Diagram indicates if a given phase in that system will be accessible under those equilibrium conditions (although metastable phases certainly may be obtainable under appropriate circumstances). Even when a stable phase is accessible, control of the stoichiometry may be difficult to achieve owing to complex phase equilibria. For example, many transition metals have a propensity to adjust their oxidation state depending on the temperature and oxygen partial pressure, which can result in a multiphase product (impurities) and/or one with mixed valency.

  It is imperative that one be able to properly interpret Phase Diagrams. In the first part of this chapter, some underlying concepts are reviewed, from thermodynamics necessary for understanding phase equilibria. The interpretation of Phase Diagrams will be subsequently taken up. Afterward, the reader will be introduced to the calculation of Phase Diagram (CALPHAD) method, in which phase equilibria predictions are made on high‐order systems by extrapolation of thermodynamic data from the lower‐order parent systems. For example, a Phase Diagram for a ternary system ABC can be predicted from the AB, BC, and AC

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  Solid State Materials Chemistry

  • Patrick M. Woodward, Pavel Karen, John S. O. Evans, Thomas Vogt(Authors)
  • 2021(Publication Date)
  • Cambridge University Press

    (Publisher)

  4 Phase Diagrams and Phase Transitions In this chapter we will consider two separate but related topics; Phase Diagrams and phase transitions. Phase Diagrams are used throughout materials chemistry to guide the synthesis of known and new materials. Electronic and magnetic Phase Diagrams are used to help summarize the properties of functional materials under different conditions. We’ll see throughout the later chapters of this book that many functional materials undergo structural phase transitions that are intimately linked to their properties. The second half of this chapter will introduce the fundamental concepts needed to understand these. 4.1 Phase Diagrams Phase Diagrams provide a graphical summary of the behavior of chemical systems at equilibrium as a function of external variables. In materials chemistry, these variables are usually composition, temperature, and pressure, but could also include effects such as electric or magnetic field. These diagrams are based on the phase rule first proposed by Gibbs, which states that for a system in equilibrium: P þ F ¼ C þ 2 (4.1) where P is the number of phases, F the degrees of freedom or variance, and C the number of components. 1 We can define the system as being the part of the universe that we’re interested 1 The derivation of this rule is relatively straightforward and is covered in many physical chemistry texts. Briefly, to describe the state of a system consisting of P phases, you need temperature, pressure (two variables), and (P·C) − P mole fractions for P phases of C components each (−P appears because the sum of mole fractions of each phase is one, hence one fraction per phase is redundant). There are then a total of 2 + (P·C) − P variables. For phases at equilibrium, chemical potentials for each component must be equal. This gives C(P − 1) independent equations (conditions).

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  Physical Metallurgy

  Metals, Alloys, Phase Transformations

  • Vadim M. Schastlivtsev, Vitaly I. Zel'dovich(Authors)
  • 2022(Publication Date)
  • De Gruyter

    (Publisher)

  Chapter 2  Phase Diagrams

  Phase Diagrams play an important role in physical metallurgy. They serve as the basis for analyzing phase transformations and forming the structure of alloys when changing their chemical composition, temperature, and pressure. Let us first resort to definitions of the concepts used further in this chapter. An alloy is referred to as a mixture obtained by fusing two or more elements where at least one of them is metal. Components are called chemically individual substances combined into an alloy. Components can be both elements and chemical compounds. A phase is the homogeneous part (solid and liquid) of an alloy, isolated from another parts by a separation surface demarcating discontinuous change in alloy properties. In real alloys, the phase includes a set of homogeneous alloy parts having a separation surface (interphase boundaries). Equilibrium of the phases is reached when there are no visible transformations in an alloy. In other words and more precisely, an alloy is in a state of thermodynamic equilibrium if its state parameters (temperature, pressure, and concentration) do not change over time and if there are no fluxes of any type. From a microscopic point of view, such a state is a state of dynamic (mobile) equilibrium. A Phase Diagram involves a graphic representation of the equilibrium states of the phases in the system of a given group of alloys.

  2.1  The phase rule

  The conditions of equilibrium of the phases in an alloy are satisfied when chemical potentials of each component in any of the phases are said to be equal. If a given component in one phase has the chemical potential greater than in the other phase, it passes to a phase with lower chemical potential. The condition of minimum thermodynamic potential dictates the equality of the chemical potentials of each component in all phases being in equilibrium. Let k

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  High Temperature Phase Equilibria and Phase Diagrams

  • Chu-Kun Kuo, Zu-Xiang Lin, Dong-Sheng Yan(Authors)
  • 2017(Publication Date)
  • Pergamon

    (Publisher)

  These Phase Diagrams are usually included in both compilations of the inorganic molten salts and of high temperature ceramic systems. In addition, some oxide systems may be of interest in different scientific and technological disciplines. So far the phase equilibrium and Phase Diagram data are widely used in petrology, ceramics, metallurgy, chemistry and crystal growth science. Comprehensive reviews of the applications were made in a number of books and publications. Particularly, relations have been currently established between the Phase Diagram studies and diverse solid state materials. The phase equilibria and Phase Diagram data have been found to be of importance in preparing and improving the existing materials as well as to searching for new material systems. Generally speaking, a Phase Diagram can convey information about: (1) Formation, composition range and stabihty of intermediate com-pounds. (2) Melting behaviour between mixtures and the crystallization path of melt. (3) Route of chemical reactions between the components. (4) Solubility limits and phase separation in condensed mixtures. ( 5 ) Equilibria between gases and condensed matter. (6) Stability field of solid phases and their transformations. 108 High temperature phase equilibria and Phase Diagrams 4.2 CO-ORDINATION T R A N S F O R M A T I O N FOR COMPOSITIONAL POINTS 4.2.1 R e p r e s e n t a t i o n of c o m p o s i t i o n a l points As described in sections 2.4.2 and 2.5.1 a given composition is located in a binary or ternary system by the Lever rule or the centre of gravity of triangle rule. Basically a point in a multicomponent system can be represented by a co-ordinate system established by the end members of the system. The mathematical expressions are written as follows: (1) Two-component system (Fig. 4.1). If a point Ρ is in the binary system N^-Nj, its composition can be represented by a couple of binary (7) Effects of temperature and pressure on equilibria.

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  Fundamentals of Materials Science and Engineering

  An Integrated Approach

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  Thus, it is important to understand not only equilibrium states and structures, but also the speed or rate at which they are established and the factors that affect the rate. This chapter is devoted almost exclusively to equilibrium structures; the treatment of reaction rates and nonequilibrium structures is deferred to Chapter 12. phase equilibrium metastable Much of the information about the control of the phase structure of a particular system is conveniently and concisely displayed in what is called a Phase Diagram, also often termed an equilibrium diagram. Three externally controllable parameters affect phase structure—temperature, pressure, and composition—and Phase Diagrams are constructed when various combinations of these parameters are plotted against one another. Perhaps the simplest and easiest type of Phase Diagram to understand is that for a one-component system, in which composition is held constant (i.e., the Phase Diagram is for a pure substance); this means that pressure and temperature are the variables. This one-component Phase Diagram (or unary Phase Diagram, sometimes also called a pressure–temperature [or P–T ] diagram) is represented as a two-dimensional plot of Phase Diagram 11.6 | | ONE-COMPONENT (OR UNARY) Phase DiagramS Concept Check 11.1 What is the difference between the states of phase equilibrium and metastability? [The answer may be found on the product page at www.wiley.com ] 446  Chapter 11 Phase Diagrams Binary Phase Diagrams pressure (ordinate, or vertical axis) versus temperature (abscissa, or horizontal axis). Most often, the pressure axis is scaled logarithmically. We illustrate this type of Phase Diagram and demonstrate its interpretation using as an example the one for H 2 O, which is shown in Figure 11.2. Regions for three different phases—solid, liquid, and vapor—are delineated on the plot. Each of the phases exists un- der equilibrium conditions over the temperature–pressure ranges of its corresponding area.

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  Fundamentals of Materials Science and Engineering

  An Integrated Approach

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  380 • C h a p t e r 10 Phase Diagrams The accompanying graph is the Phase Diagram for pure H 2 O. Parameters plotted are external pressure (vertical axis, scaled logarithmically) versus temperature. In a sense this diagram is a map in which regions for the three familiar phases—solid (ice), liquid (water), and vapor (steam)—are delineated. The three red curves represent phase boundaries that define the regions. A photograph located in each region shows an example of its phase—ice cubes, liquid water being poured into a glass, and steam spewing from a kettle. (Photographs courtesy of iStockphoto.) Liquid (Water) Pressure (atm) Vapor (Steam) 1,000 100 10 1.0 0.1 0.01 0.001 −20 20 40 60 80 100 120 0 Solid (Ice) Temperature (°C) Three phases for the H 2 O system are shown in this photograph: ice (the iceberg), water (the ocean or sea), and vapor (the clouds). These three phases are not in equilibrium with one another. © Achim Baqué/Stockphoto/ • 381 WHY STUDY Phase Diagrams? One reason that a knowledge and understanding of Phase Diagrams is important to the engineer relates to the design and control of heat-treating procedures; some properties of materials are functions of their microstructures and, consequently, of their thermal histories. Even though most Phase Diagrams represent stable (or equilibrium) states and microstructures, they are nevertheless useful in understanding the develop- ment and preservation of nonequilibrium structures and their attendant properties; it is often the case that these properties are more desirable than those associated with the equilibrium state. This is aptly illustrated by the phenomenon of precipitation hardening (Sections 11.10 and 11.11). Learning Objectives After studying this chapter, you should be able to do the following: 1. (a) Schematically sketch simple isomorphous and eutectic Phase Diagrams. (b) On these diagrams, label the various phase regions.

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  Fundamentals of Materials Science and Engineering

  An Integrated Approach

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  The understanding of Phase Diagrams for alloy systems is extremely important because there is a strong correlation between microstructure and mechanical properties, and the development of microstructure of an alloy is related to the characteristics of its Phase Diagram. In addition, Phase Diagrams provide valuable information about melting, cast- ing, crystallization, and other phenomena. This chapter presents and discusses the following topics: (1) terminology associated with Phase Diagrams and phase transformations; (2) pressure–temperature Phase Diagrams for pure materials; (3) the interpretation of Phase Diagrams; (4) some of the common and relatively simple binary Phase Diagrams, including that for the iron–carbon system; and (5) the development of equilibrium microstructures upon cooling for several situations. 10.1 INTRODUCTION Definitions and Basic Concepts It is necessary to establish a foundation of definitions and basic concepts relating to alloys, phases, and equilibrium before delving into the interpretation and utilization of Phase Diagrams. The term component is frequently used in this discussion; components are pure metals and/or compounds of which an alloy is composed. For example, in a copper–zinc component • 337 338 • Chapter 10 / Phase Diagrams brass, the components are Cu and Zn. Solute and solvent, which are also common terms, were defined in Section 5.4. Another term used in this context is system, which has two meanings. System may refer to a specific body of material under consideration (e.g., a ladle of molten steel), or it may relate to the series of possible alloys consisting of the same components but without regard to alloy composition (e.g., the iron–carbon system). The concept of a solid solution was introduced in Section 5.4.

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  Phase Equilibria in Chemical Engineering

  • Stanley M. Walas(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  The pressures employed in these and the few other investigations of this type that have been made are somewhat out of the range of ordinary processing of condensed phases, but it is nevertheless interesting to have the information. 5.4.6. Equilibrium and Reality A Phase Diagram represents conditions of equilibrium. Trans- formations in the solid phase at lower temperatures may be particularly slow and unless some way can be found to speed up attainment of equilibrium, the investigation may not be practicable. Figures 5.25(d) and (e) are two of the few cases that have been investigated of solid-phase equilibria. Temper- atures should be made as high as possible and the necessary time allowed. Some solid-phase transformations can be accelerated by introducing a melting step. For instance, with a system like that of Figure 5.23(g), the solid solution con- taining 25% thallium nitrate could not be prepared by an impatient individual by mixing the ingredients at room temperature in the proper proportions. If the mixture were melted at 300 C, however, and then cooled slowly below 285 C, the solid solution would be obtained. Below eutectic temperatures, unfortunately, such tricks are not applicable. Also, since rates of solid transformations are predominantly diffusion-controlled, it is unlikely that they can be catalyzed by traces of foreign materials. Thus time and temperature are the only controls available. 5.5. TERNARY SYSTEMS Planar diagrams of ternary systems at constant T and P are composition diagrams showing regions, lines, and points at which different phases exist. Compositions of phases in equilibrium may be connected with tie-lines (connodals), but for interpolation purposes and to reduce the clutter on a small diagram some kind of continuous tie-line correlation is preferred.

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  Handbook of Superconductivity

  • Charles K. Poole, Horacio A. Farach, Richard J. Creswick(Authors)
  • 1999(Publication Date)
  • Academic Press

    (Publisher)

  In binary diagrams without solid solutions, it is a straight line, or a combination of straight lines representing constant tempera- 628 Chapter 14: Phase Diagrams tures, and with solid solutions, it is a curved line or a combination of curved and straight lines. Likewise, in ternary systems, the solidus is represented by flat planes or by curved surfaces. A phase is any portion, including the whole, of a system that is physically homogeneous within itself and bounded by a surface that mechanically separates it from any other portions. The components (of a system) are the smallest number of independently variable chemical constituents necessary and sufficient to express the composi- tion of each phase present in any state of equilibrium. Zero and negative quantities of the components are permissible in expressing the composition of a phase. The phase rule states that, for a system in equilibrium, the sum of the number of phases (P) plus a number of degress of freedom (F) must equal the sum of the number of components (C) plus 2, or P + F = C + 2. The number of degrees of freedom of a system is the number of intensive variables that can be altered independently or arbitrarily without bringing about the disappearance of a phase or the formation of a new one. Intensive variables are those that are independent of mass, such as pressure, temperature, and composition. A join (tie-line) is the region of a Phase Diagram representing all mixtures that can be formed from a given number of selected compositions. A join may be a line (binary), a surface (ternary), etc., depending on the number of selected compositions, which need not be compounds. Each selected composition, however, must be incapable of formation from the others.

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  Materials Science and Engineering

  An Introduction

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  256 • Chapter 9 / Phase Diagrams Binary Phase Diagrams pressure (ordinate, or vertical axis) versus temperature (abscissa, or horizontal axis). Most often, the pressure axis is scaled logarithmically. We illustrate this type of Phase Diagram and demonstrate its interpretation using as an example the one for H 2 O, which is shown in Figure 9.2. Regions for three different phases—solid, liquid, and vapor—are delineated on the plot. Each of the phases exist under equilibrium conditions over the temperature–pressure ranges of its corresponding area. The three curves shown on the plot (labeled aO, bO, and cO) are phase boundaries; at any point on one of these curves, the two phases on either side of the curve are in equilibrium (or coexist) with one another. Equilibrium between solid and vapor phases is along curve aO; it is likewise for the solid–liquid boundary, curve bO, and the liquid–vapor boundary, curve cO. Upon crossing a boundary (as temperature and/or pressure is altered), one phase transforms into another. For example, at 1 atm pressure, during heating the solid phase transforms to the liquid phase (i.e., melting occurs) at the point labeled 2 on Figure 9.2 (i.e., the intersection of the dashed horizontal line with the solid–liquid phase boundary); this point corresponds to a temperature of 0°C. The reverse transformation (liquid-to-solid, or solidification) takes place at the same point upon cooling. Similarly, at the intersection of the dashed line with the liquid–vapor phase boundary (point 3 in Figure 9.2, at 100°C) the liquid transforms into the vapor phase (or vaporizes) upon heating; condensation occurs for cooling. Finally, solid ice sublimes or vaporizes upon crossing the curve labeled aO. As may also be noted from Figure 9.2, all three of the phase boundary curves intersect at a common point, which is labeled O (for this H 2 O system, at a temperature of 273.16 K and a pressure of 6.04 × 10 −3 atm).

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  Callister's Materials Science and Engineering

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  276 • Chapter 9 / Phase Diagrams Binary Phase Diagrams pressure (ordinate, or vertical axis) versus temperature (abscissa, or horizontal axis). Most often, the pressure axis is scaled logarithmically. We illustrate this type of Phase Diagram and demonstrate its interpretation using as an example the one for H 2 O, which is shown in Figure 9.2. Regions for three different phases—solid, liquid, and vapor—are delineated on the plot. Each of the phases exist under equilibrium conditions over the temperature–pressure ranges of its corresponding area. The three curves shown on the plot (labeled aO, bO, and cO) are phase boundaries; at any point on one of these curves, the two phases on either side of the curve are in equilibrium (or coexist) with one another. Equilibrium between solid and vapor phases is along curve aO; it is likewise for the solid–liquid boundary, curve bO, and the liquid–vapor boundary, curve cO. Upon crossing a boundary (as temperature and/or pressure is altered), one phase transforms into another. For example, at 1 atm pressure, during heating the solid phase transforms to the liquid phase (i.e., melting occurs) at the point labeled 2 on Figure 9.2 (i.e., the intersection of the dashed horizontal line with the solid–liquid phase boundary); this point corresponds to a temperature of 0°C. The reverse transformation (liquid-to-solid, or solidification) takes place at the same point upon cooling. Similarly, at the intersection of the dashed line with the liquid–vapor phase boundary (point 3 in Figure 9.2, at 100°C) the liquid transforms into the vapor phase (or vaporizes) upon heating; condensation occurs for cooling. Finally, solid ice sublimes or vaporizes upon crossing the curve labeled aO. As may also be noted from Figure 9.2, all three of the phase boundary curves intersect at a common point, which is labeled O (for this H 2 O system, at a temperature of 273.16 K and a pressure of 6.04 × 10 −3 atm).

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