DOCSLIB.ORG

Phase Diagrams, Solid Solutions, Phase Transformations

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Phase Diagrams, Solid Solutions, Phase Transformations Phase Diagrams, Solid Solutions, Phase Strengthening, Phase Transformations Components and Phases • Components: The elements or compounds that are mixed initially (Al and Cu). • Phases: A phase is a homogenous, physically distinct and mechanically separable portion of the material with a given chemical composition and structure (a and b). Aluminum- (lighter Copper phase) Alloy (darker phase) 2 Solid solution A solution that contains two or more types of atoms or ions that are dispersed uniformly throughout the material Solute The impurities that may occupy regular lattice sites in the crystal or interstitial sites Alloys A material made from multiple elements that exhibits properties of a metallic material Stainless steels Alloys that usually contain iron (Fe), carbon (C), chromium (Cr), nickel (Ni), and some other elements Single-phase alloy An alloy consisting of one phase Multiple-phase alloy An alloy that consists of two or more phases Chapter 10: Solid Solutions and Phase Equilibrium Figure 10.2 © 2011 Cengage Learning Engineering. All Rights Reserved. 10 - 4 Phase Equilibria: Solubility Limit • Solution – solid, liquid, or gas solutions, single phase • Mixture – more than one phase Sugar/Water Phase Diagram • Solubility Limit: Maximum concentration for 100 Solubility which only a single phase ) L C 80 Limit ° solution exists. ( (liquid) e r 60 u + t L Question: What is the a r S solubility limit for sugar in e 40 (liquid solution p i.e., syrup) m (solid water at 20°C? e T 20 sugar) Answer: 65 wt% sugar. At 20°C, if C < 65 wt% sugar: syrup 0 20 40 6065 80 100 r r At 20°C, if C > 65 wt% sugar: syrup + sugar e C = Composition (wt% sugar) t a a g u W S Equilibrium • A system is at equilibrium if its free energy is at a minimum, given a specified combination of temperature, pressure and composition. • The (macroscopic) characteristics of the system do not change with time — the system is stable. • A change in T, P or C for the system will result in an increase in the free energy and possible changes to another state whereby the free energy is lowered. 6 Chapter 10: Solid Solutions and Phase Equilibrium Conditions for Unlimited Solid Solubility . Hume-Rothery rules . Size factor – The atoms or ions must be of similar size, with no more than a 15% difference in atomic radius, in order to minimize the lattice strain. Crystal structure – The materials must have the same crystal structure. Valence – The ions must have the same valence. Electronegativity – The atoms must have approximately the same electronegativity. 10 - 8 © 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 10: Solid Solutions and Phase Equilibrium Figure 10.3 10 - 10 © 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 10: Solid Solutions and Phase Equilibrium Solubility and Solid Solutions . Polymeric systems . Copolymer: A polymer that is formed by combining two or more different types of monomers, usually with the idea of blending the properties affiliated with individual polymers. For example, acrylonitrile (A), butadiene (B), and styrene (S) monomers can be made to react to form a copolymer known as ABS. 10 - 11 © 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 10: Solid Solutions and Phase Equilibrium Solid-Solution Strengthening . Solid-solution strengthening . Increasing the strength of a metallic material via the formation of a solid solution. 10 - 12 © 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 10: Solid Solutions and Phase Equilibrium Figure 10.8 10 - 13 © 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 10: Solid Solutions and Phase Equilibrium Isomorphous Phase Diagrams . Phase diagram . Indicate phases as a function of Temp., Comp. and Pressure (under equilibrium condition) . Binary phase diagram . A phase diagram for a system with two components. Isomorphous phase diagram . A phase diagram in which the components display unlimited solid solubility. 10 - 14 © 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 10: Solid Solutions and Phase Equilibrium Figure 10.9 10 - 15 © 2011 Cengage Learning Engineering. All Rights Reserved. Determination of phase(s) present • Rule 1: If we know T and Co, then we know: --how many phases and which phases are present. T(°C) 1600 • Examples: 1500 L (liquid) A(1100, 60): s ) du 5 ui 1 phase: 3 q 1400 , li us 0 id 5 ol Cu-Ni B(1250, 35): 2 s 1 phase ( 1300 + 2 phases: L + B L (FCC solid diagram 1200 solution) 1100 A(1100,60) Melting points: Cu = 1085°C, Ni = 1453 °C 1000 0 20 40 60 80 100 wt% Ni Solidus - Temperature where alloy is completely solid. Above this line, liquefaction begins. Liquidus - Temperature where alloy is completely liquid. Below this line, solidification begins. 16 Phase Diagrams: composition of phases • Rule 2: If we know T and Co, then we know: --the composition of each phase. Cu-Ni system • Examples: T(°C) A T tie line A dus At TA = 1320°C: qui 1300 L (liquid) li Only Liquid (L) present + L s C = C ( = 35 wt% Ni) B lidu L 0 TB so At TD = 1190°C: + Only Solid (a) present 1200 L D (solid) T Ca = C0 ( = 35 wt% Ni) D 20 30 40 50 At TB = 1250°C: 3235 43 C C C Both and L present L o wt% Ni a CL = C liquidus ( = 32 wt% Ni) Ca = C solidus ( = 43 wt% Ni) 17 Phase Diagrams: weight fractions of phases • Rule 3: If we know T and Co, then we know: --the amount of each phase (given in wt%). • Examples: Co = 35wt%Ni T(°C) Cu-Ni system At T A: Only Liquid (L) A TA tie line s WL = 100wt%, W = 0 idu iqu At T D: Only Solid ( ) 1300 L (liquid) l + L s WL = 0, W = 100wt% B lidu TB so At T B: Both and L R S + 1200 L S D (solid) W CS Co 43S 35 TD R WWL 73wt % LL R S 43 32 CRSCL R S 20 3032R35 S4043 50 CLCo C R wt% Ni C Co S W CRo CL R W W R S = 27wt % L R S R S C CL C CL R S 18 Chapter 10: Solid Solutions and Phase Equilibrium Figure 10.15 10 - 19 © 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 10: Solid Solutions and Phase Equilibrium Figure 10.16 10 - 20 © 2011 Cengage Learning Engineering. All Rights Reserved. Chapter 10: Solid Solutions and Phase Equilibrium Figure 10.17 10 - 21 © 2011 Cengage Learning Engineering. All Rights Reserved. Importance of Phase Diagrams • There is a strong correlation between microstructure and mechanical properties, and the development of alloy microstructure is related to the characteristics of its phase diagram. • Phase diagrams provide valuable information about melting, casting, crystallization and other phenomena. 22 Microstructure • In metal alloys, microstructure is characterized by the number of phases, their proportions, and the way they are arranged. • The microstructure depends on: – Alloying elements – Concentration – Heat treatment (temperature, time, rate of cooling) 23 Eutectic • A eutectic or eutectic mixture is a mixture of two or more phases at a composition that has the lowest melting point. • It is where the phases simultaneously crystallize from molten solution. • The proper ratios of phases to obtain a eutectic is identified by the eutectic point on a binary phase diagram. • The term comes from the Greek 'eutektos', meaning 'easily melted.‘ 24 •The phase diagram displays a simple binary system composed of two components, A and B, which has a eutectic point. •The phase diagram plots relative concentrations of A and B along the X-axis, and temperature along the Y-axis. The eutectic point is the point where the liquid phase borders directly on the solid α + β phase; it represents the minimum melting temperature of any possible A B alloy. •The temperature that corresponds to this point is known as the eutectic temperature. •Not all binary system alloys have a eutectic point: those that form a solid solution at all concentrations, such as the gold-silver system, have no eutectic. An alloy system that has a eutectic is often referred to as a eutectic system, or eutectic alloy. •Solid products of a eutectic transformation can often be identified by their lamellar structure, as opposed to the dendritic structures commonly seen in non-eutectic solidification. 25 Binary-Eutectic Systems has a special composition 2 components with a min. melting T. T(°C) Cu-Ag system 1200 • 3 single phase regions L (liquid) (L, a, b) 1000 • Limited solubility: a L + a T 800 779°C L+b b a: mostly Cu E 8.0 71.9 91.2 b: mostly Ag 600 • TE : No liquid below TE a + b 400 • CE : Composition at temperature TE 200 0 20 40 60 C 80 100 Eutectic reaction E • C , wt% Ag L(CE) a(CaE) + b(CbE) cooling L(71.9 wt% Ag) (8.0 wt% Ag) (91.2 wt% Ag) 26 heating Pb-Sn Phasec10f08 Diagram Liquidus Solidus Solidus Solidus Solvus Solvus Lamellar Eutectic Structure A 2-phase microstructure resulting from the solidification of a liquid having the eutectic composition where the phases exist as a lamellae that alternate with one Pb-rich another. Formation of eutectic Sn-rich layered microstructure in the Pb-Sn system during solidification at the eutectic composition. Compositions of α and β phases are very different. Solidification involves redistribution of Pb and Sn atoms by atomic diffusion. 28 Pb-Sn Microstructures The dark layers are Pb-rich α phase, the light layers are the Sn- rich β phase. 29 Iron-Carbon System • Pure iron when heated experiences 2 changes in crystal structure before it melts. • At room temperature the stable form, ferrite (a iron) has a BCC crystal structure.
Load more

Recommended publications
  • Lecture Notes: BCS Theory of Superconductivity
    Lecture Notes: BCS theory of superconductivity Prof. Rafael M. Fernandes Here we will discuss a new ground state of the interacting electron gas: the superconducting state. In this macroscopic quantum state, the electrons form coherent bound states called Cooper pairs, which dramatically change the macroscopic properties of the system, giving rise to perfect conductivity and perfect diamagnetism. We will mostly focus on conventional superconductors, where the Cooper pairs originate from a small attractive electron-electron interaction mediated by phonons. However, in the so- called unconventional superconductors - a topic of intense research in current solid state physics - the pairing can originate even from purely repulsive interactions. 1 Phenomenology Superconductivity was discovered by Kamerlingh-Onnes in 1911, when he was studying the transport properties of Hg (mercury) at low temperatures. He found that below the liquifying temperature of helium, at around 4:2 K, the resistivity of Hg would suddenly drop to zero. Although at the time there was not a well established model for the low-temperature behavior of transport in metals, the result was quite surprising, as the expectations were that the resistivity would either go to zero or diverge at T = 0, but not vanish at a finite temperature. In a metal the resistivity at low temperatures has a constant contribution from impurity scattering, a T 2 contribution from electron-electron scattering, and a T 5 contribution from phonon scattering. Thus, the vanishing of the resistivity at low temperatures is a clear indication of a new ground state. Another key property of the superconductor was discovered in 1933 by Meissner.
    [Show full text]
  • Supercritical Fluid Extraction of Positron-Emitting Radioisotopes from Solid Target Matrices
    XA0101188 11. United States of America Supercritical Fluid Extraction of Positron-Emitting Radioisotopes From Solid Target Matrices D. Schlyer, Brookhaven National Laboratory, Chemistry Department, Upton, Bldg. 901, New York 11973-5000, USA Project Description Supercritical fluids are attractive as media for both chemical reactions, as well as process extraction since their physical properties can be manipulated by small changes in pressure and temperature near the critical point of the fluid. What is a supercritical fluid? Above a certain temperature, a vapor can no longer be liquefied regardless of pressure critical temperature - Tc supercritical fluid r«gi on solid a u & temperature Fig. 1. Phase diagram depicting regions of solid, liquid, gas and supercritical fluid behavior. The critical point is defined by a critical pressure (Pc) and critical temperature (Tc) for a particular substance. Such changes can result in drastic effects on density-dependent properties such as solubility, refractive index, dielectric constant, viscosity and diffusivity of the fluid[l,2,3]. This suggests that pressure tuning of a pure supercritical fluid may be a useful means to manipulate chemical reactions on the basis of a thermodynamic solvent effect. It also means that the solvation properties of the fluid can be precisely controlled to enable selective component extraction from a matrix. In recent years there has been a growing interest in applying supercritical fluid extraction to the selective removal of trace metals from solid samples [4-10]. Much of the work has been done on simple systems comprised of inert matrices such as silica or cellulose. Recently, this process as been expanded to environmental samples as well [11,12].
    [Show full text]
  • Recent Progress on Deep Eutectic Solvents in Biocatalysis Pei Xu1,2, Gao‑Wei Zheng3, Min‑Hua Zong1,2, Ning Li1 and Wen‑Yong Lou1,2*
    Xu et al. Bioresour. Bioprocess. (2017) 4:34 DOI 10.1186/s40643-017-0165-5 REVIEW Open Access Recent progress on deep eutectic solvents in biocatalysis Pei Xu1,2, Gao‑Wei Zheng3, Min‑Hua Zong1,2, Ning Li1 and Wen‑Yong Lou1,2* Abstract Deep eutectic solvents (DESs) are eutectic mixtures of salts and hydrogen bond donors with melting points low enough to be used as solvents. DESs have proved to be a good alternative to traditional organic solvents and ionic liq‑ uids (ILs) in many biocatalytic processes. Apart from the benign characteristics similar to those of ILs (e.g., low volatil‑ ity, low infammability and low melting point), DESs have their unique merits of easy preparation and low cost owing to their renewable and available raw materials. To better apply such solvents in green and sustainable chemistry, this review frstly describes some basic properties, mainly the toxicity and biodegradability of DESs. Secondly, it presents several valuable applications of DES as solvent/co-solvent in biocatalytic reactions, such as lipase-catalyzed transester‑ ifcation and ester hydrolysis reactions. The roles, serving as extractive reagent for an enzymatic product and pretreat‑ ment solvent of enzymatic biomass hydrolysis, are also discussed. Further understanding how DESs afect biocatalytic reaction will facilitate the design of novel solvents and contribute to the discovery of new reactions in these solvents. Keywords: Deep eutectic solvents, Biocatalysis, Catalysts, Biodegradability, Infuence Introduction (1998), one concept is “Safer Solvents and Auxiliaries”. Biocatalysis, defned as reactions catalyzed by bio- Solvents represent a permanent challenge for green and catalysts such as isolated enzymes and whole cells, has sustainable chemistry due to their vast majority of mass experienced signifcant progress in the felds of either used in catalytic processes (Anastas and Eghbali 2010).
    [Show full text]
  • Equation of State and Phase Transitions in the Nuclear
    National Academy of Sciences of Ukraine Bogolyubov Institute for Theoretical Physics Has the rights of a manuscript Bugaev Kyrill Alekseevich UDC: 532.51; 533.77; 539.125/126; 544.586.6 Equation of State and Phase Transitions in the Nuclear and Hadronic Systems Speciality 01.04.02 - theoretical physics DISSERTATION to receive a scientific degree of the Doctor of Science in physics and mathematics arXiv:1012.3400v1 [nucl-th] 15 Dec 2010 Kiev - 2009 2 Abstract An investigation of strongly interacting matter equation of state remains one of the major tasks of modern high energy nuclear physics for almost a quarter of century. The present work is my doctor of science thesis which contains my contribution (42 works) to this field made between 1993 and 2008. Inhere I mainly discuss the common physical and mathematical features of several exactly solvable statistical models which describe the nuclear liquid-gas phase transition and the deconfinement phase transition. Luckily, in some cases it was possible to rigorously extend the solutions found in thermodynamic limit to finite volumes and to formulate the finite volume analogs of phases directly from the grand canonical partition. It turns out that finite volume (surface) of a system generates also the temporal constraints, i.e. the finite formation/decay time of possible states in this finite system. Among other results I would like to mention the calculation of upper and lower bounds for the surface entropy of physical clusters within the Hills and Dales model; evaluation of the second virial coefficient which accounts for the Lorentz contraction of the hard core repulsing potential between hadrons; inclusion of large width of heavy quark-gluon bags into statistical description.
    [Show full text]
  • Homework 5 Solutions
    SCI 1410: materials science & solid state chemistry HOMEWORK 5. solutions Textbook Problems: Imperfections in Solids 1. Askeland 4-67. Why is most “gold” or “silver” jewelry made out of gold or silver alloyed with copper, i.e, what advantages does copper offer? We have two major considerations in jewelry alloying: strength and cost. Copper additions obviously lower the cost of gold or silver (Note that 14K gold is actually only about 50% gold). Copper and other alloy additions also strengthen pure gold and pure silver. In both gold and silver, copper will strengthen the material by either solid solution strengthening (substitutional Cu atoms in the Au or Ag crystal), or by formation of second phase in the microstructure. 2. Solid state solubility. Of the elements in the chart below, name those that would form each of the following relationships with copper (non-metals only have atomic radii listed): a. Substitutional solid solution with complete solubility o Ni and possibly Ag, Pd, and Pt b. Substitutional solid solution of incomplete solubility o Ag, Pd, and Pt (if you didn’t include these in part (a); Al, Co, Cr, Fe, Zn c. An interstitial solid solution o C, H, O (small atomic radii) Element Atomic Radius (nm) Crystal Structure Electronegativity Valence Cu 0.1278 FCC 1.9 +2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Pd 0.1376 FCC 2.2 +2 Pt 0.1387 FCC 2.2 +2 Zn 0.1332 HCP 1.6 +2 3.
    [Show full text]
  • Lecture 15: 11.02.05 Phase Changes and Phase Diagrams of Single- Component Materials
    3.012 Fundamentals of Materials Science Fall 2005 Lecture 15: 11.02.05 Phase changes and phase diagrams of single- component materials Figure removed for copyright reasons. Source: Abstract of Wang, Xiaofei, Sandro Scandolo, and Roberto Car. "Carbon Phase Diagram from Ab Initio Molecular Dynamics." Physical Review Letters 95 (2005): 185701. Today: LAST TIME .........................................................................................................................................................................................2� BEHAVIOR OF THE CHEMICAL POTENTIAL/MOLAR FREE ENERGY IN SINGLE-COMPONENT MATERIALS........................................4� The free energy at phase transitions...........................................................................................................................................4� PHASES AND PHASE DIAGRAMS SINGLE-COMPONENT MATERIALS .................................................................................................6� Phases of single-component materials .......................................................................................................................................6� Phase diagrams of single-component materials ........................................................................................................................6� The Gibbs Phase Rule..................................................................................................................................................................7� Constraints on the shape of
    [Show full text]
  • Chapter 15: Solutions
    452-487_Ch15-866418 5/10/06 10:51 AM Page 452 CHAPTER 15 Solutions Chemistry 6.b, 6.c, 6.d, 6.e, 7.b I&E 1.a, 1.b, 1.c, 1.d, 1.j, 1.m What You’ll Learn ▲ You will describe and cate- gorize solutions. ▲ You will calculate concen- trations of solutions. ▲ You will analyze the colliga- tive properties of solutions. ▲ You will compare and con- trast heterogeneous mixtures. Why It’s Important The air you breathe, the fluids in your body, and some of the foods you ingest are solu- tions. Because solutions are so common, learning about their behavior is fundamental to understanding chemistry. Visit the Chemistry Web site at chemistrymc.com to find links about solutions. Though it isn’t apparent, there are at least three different solu- tions in this photo; the air, the lake in the foreground, and the steel used in the construction of the buildings are all solutions. 452 Chapter 15 452-487_Ch15-866418 5/10/06 10:52 AM Page 453 DISCOVERY LAB Solution Formation Chemistry 6.b, 7.b I&E 1.d he intermolecular forces among dissolving particles and the Tattractive forces between solute and solvent particles result in an overall energy change. Can this change be observed? Safety Precautions Dispose of solutions by flushing them down a drain with excess water. Procedure 1. Measure 10 g of ammonium chloride (NH4Cl) and place it in a Materials 100-mL beaker. balance 2. Add 30 mL of water to the NH4Cl, stirring with your stirring rod.
    [Show full text]
  • Self-Assembly of a Colloidal Interstitial Solid Solution with Tunable Sublattice Doping: Supplementary Information
    Self-assembly of a colloidal interstitial solid solution with tunable sublattice doping: Supplementary information L. Filion,∗ M. Hermes, R. Ni, E. C. M. Vermolen,† A. Kuijk, C. G. Christova,‡ J. C. P. Stiefelhagen, T. Vissers, A. van Blaaderen, and M. Dijkstra Soft Condensed Matter, Debye Institute for NanoMaterials Science, Utrecht University, Princetonplein 1, NL-3584 CC Utrecht, the Netherlands I. CRYSTAL STRUCTURE LS6 In the main paper we use full free-energy calculations to determine the phase diagram for binary mixtures of hard spheres with size ratio σS/σL = 0.3 where σS(L) is the diameter of the small (large) particles. The phases we considered included a structure with LS6 stoichiometry for which we could not identify an atomic analogue. Snapshots of this structure from various perspectives are shown in Fig. S1. FIG. S1: Unit cell of the binary LS6 superlattice structure described in this paper. Note that both species exhibit long-range crystalline order. The unit cell is based on a body-centered-cubic cell of the large particles in contrast to the face-centered-cubic cell associated with the interstitial solid solution covering most of the phase diagram (Fig. 1). II. PHASE DIAGRAM AT CONSTANT VOLUME 3 In the main paper, we present the xS − p representation of the phase diagram where p = βPσL is the reduced pressure, xS = NS/(NS + NL), NS(L) is the number of small (large) hard spheres, β = 1/kBT , kB is the Boltzmann constant, and T is the absolute temperature. This is the natural representation arising from common tangent construc- tions at constant pressure and the representation required for further simulation studies such as nucleation studies.
    [Show full text]
  • Solid Solution Softening and Enhanced Ductility in Concentrated FCC Silver Solid Solution Alloys
    UC Irvine UC Irvine Previously Published Works Title Solid solution softening and enhanced ductility in concentrated FCC silver solid solution alloys Permalink https://escholarship.org/uc/item/7d05p55k Authors Huo, Yongjun Wu, Jiaqi Lee, Chin C Publication Date 2018-06-27 DOI 10.1016/j.msea.2018.05.057 Peer reviewed eScholarship.org Powered by the California Digital Library University of California Materials Science & Engineering A 729 (2018) 208–218 Contents lists available at ScienceDirect Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea Solid solution softening and enhanced ductility in concentrated FCC silver T solid solution alloys ⁎ Yongjun Huoa,b, , Jiaqi Wua,b, Chin C. Leea,b a Electrical Engineering and Computer Science University of California, Irvine, CA 92697-2660, United States b Materials and Manufacturing Technology University of California, Irvine, CA 92697-2660, United States ARTICLE INFO ABSTRACT Keywords: The major adoptions of silver-based bonding wires and silver-sintering methods in the electronic packaging Concentrated solid solutions industry have incited the fundamental material properties research on the silver-based alloys. Recently, an Solid solution softening abnormal phenomenon, namely, solid solution softening, was observed in stress vs. strain characterization of Ag- Twinning-induced plasticity In solid solution. In this paper, the mechanical properties of additional concentrated silver solid solution phases Localized homologous temperature with other solute elements, Al, Ga and Sn, have been experimentally determined, with their work hardening Advanced joining materials behaviors and the corresponding fractography further analyzed. Particularly, the concentrated Ag-Ga solid so- lution has been discovered to possess the best combination of mechanical properties, namely, lowest yield strength, highest ductility and highest strength, among the concentrated solid solutions of the current study.
    [Show full text]
  • Phase Diagrams
    Module-07 Phase Diagrams Contents 1) Equilibrium phase diagrams, Particle strengthening by precipitation and precipitation reactions 2) Kinetics of nucleation and growth 3) The iron-carbon system, phase transformations 4) Transformation rate effects and TTT diagrams, Microstructure and property changes in iron- carbon system Mixtures – Solutions – Phases Almost all materials have more than one phase in them. Thus engineering materials attain their special properties. Macroscopic basic unit of a material is called component. It refers to a independent chemical species. The components of a system may be elements, ions or compounds. A phase can be defined as a homogeneous portion of a system that has uniform physical and chemical characteristics i.e. it is a physically distinct from other phases, chemically homogeneous and mechanically separable portion of a system. A component can exist in many phases. E.g.: Water exists as ice, liquid water, and water vapor. Carbon exists as graphite and diamond. Mixtures – Solutions – Phases (contd…) When two phases are present in a system, it is not necessary that there be a difference in both physical and chemical properties; a disparity in one or the other set of properties is sufficient. A solution (liquid or solid) is phase with more than one component; a mixture is a material with more than one phase. Solute (minor component of two in a solution) does not change the structural pattern of the solvent, and the composition of any solution can be varied. In mixtures, there are different phases, each with its own atomic arrangement. It is possible to have a mixture of two different solutions! Gibbs phase rule In a system under a set of conditions, number of phases (P) exist can be related to the number of components (C) and degrees of freedom (F) by Gibbs phase rule.
    [Show full text]
  • Phase Transitions in Multicomponent Systems
    Physics 127b: Statistical Mechanics Phase Transitions in Multicomponent Systems The Gibbs Phase Rule Consider a system with n components (different types of molecules) with r phases in equilibrium. The state of each phase is defined by P,T and then (n − 1) concentration variables in each phase. The phase equilibrium at given P,T is defined by the equality of n chemical potentials between the r phases. Thus there are n(r − 1) constraints on (n − 1)r + 2 variables. This gives the Gibbs phase rule for the number of degrees of freedom f f = 2 + n − r A Simple Model of a Binary Mixture Consider a condensed phase (liquid or solid). As an estimate of the coordination number (number of nearest neighbors) think of a cubic arrangement in d dimensions giving a coordination number 2d. Suppose there are a total of N molecules, with fraction xB of type B and xA = 1 − xB of type A. In the mixture we assume a completely random arrangement of A and B. We just consider “bond” contributions to the internal energy U, given by εAA for A − A nearest neighbors, εBB for B − B nearest neighbors, and εAB for A − B nearest neighbors. We neglect other contributions to the internal energy (or suppose them unchanged between phases, etc.). Simple counting gives the internal energy of the mixture 2 2 U = Nd(xAεAA + 2xAxBεAB + xBεBB) = Nd{εAA(1 − xB) + εBBxB + [εAB − (εAA + εBB)/2]2xB(1 − xB)} The first two terms in the second expression are just the internal energy of the unmixed A and B, and so the second term, depending on εmix = εAB − (εAA + εBB)/2 can be though of as the energy of mixing.
    [Show full text]
  • Introduction to Phase Diagrams*
    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.
    [Show full text]