1 Solutions and Other Mixtures
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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. -
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. -
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. -
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. -
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. -
Grade 6 Science Mechanical Mixtures Suspensions
Grade 6 Science Week of November 16 – November 20 Heterogeneous Mixtures Mechanical Mixtures Mechanical mixtures have two or more particle types that are not mixed evenly and can be seen as different kinds of matter in the mixture. Obvious examples of mechanical mixtures are chocolate chip cookies, granola and pepperoni pizza. Less obvious examples might be beach sand (various minerals, shells, bacteria, plankton, seaweed and much more) or concrete (sand gravel, cement, water). Mechanical mixtures are all around you all the time. Can you identify any more right now? Suspensions Suspensions are mixtures that have solid or liquid particles scattered around in a liquid or gas. Common examples of suspensions are raw milk, salad dressing, fresh squeezed orange juice and muddy water. If left undisturbed the solids or liquids that are in the suspension may settle out and form layers. You may have seen this layering in salad dressing that you need to shake up before using them. After a rain fall the more dense particles in a mud puddle may settle to the bottom. Milk that is fresh from the cow will naturally separate with the cream rising to the top. Homogenization breaks up the fat molecules of the cream into particles small enough to stay suspended and this stable mixture is now a colloid. We will look at colloids next. Solution, Suspension, and Colloid: https://youtu.be/XEAiLm2zuvc Colloids Colloids: https://youtu.be/MPortFIqgbo Colloids are two phase mixtures. Having two phases means colloids have particles of a solid, liquid or gas dispersed in a continuous phase of another solid, liquid, or gas. -
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. -
Gp-Cpc-01 Units – Composition – Basic Ideas
GP-CPC-01 UNITS – BASIC IDEAS – COMPOSITION 11-06-2020 Prof.G.Prabhakar Chem Engg, SVU GP-CPC-01 UNITS – CONVERSION (1) ➢ A two term system is followed. A base unit is chosen and the number of base units that represent the quantity is added ahead of the base unit. Number Base unit Eg : 2 kg, 4 meters , 60 seconds ➢ Manipulations Possible : • If the nature & base unit are the same, direct addition / subtraction is permitted 2 m + 4 m = 6m ; 5 kg – 2.5 kg = 2.5 kg • If the nature is the same but the base unit is different , say, 1 m + 10 c m both m and the cm are length units but do not represent identical quantity, Equivalence considered 2 options are available. 1 m is equivalent to 100 cm So, 100 cm + 10 cm = 110 cm 0.01 m is equivalent to 1 cm 1 m + 10 (0.01) m = 1. 1 m • If the nature of the quantity is different, addition / subtraction is NOT possible. Factors used to check equivalence are known as Conversion Factors. GP-CPC-01 UNITS – CONVERSION (2) • For multiplication / division, there are no such restrictions. They give rise to a set called derived units Even if there is divergence in the nature, multiplication / division can be carried out. Eg : Velocity ( length divided by time ) Mass flow rate (Mass divided by time) Mass Flux ( Mass divided by area (Length 2) – time). Force (Mass * Acceleration = Mass * Length / time 2) In derived units, each unit is to be individually converted to suit the requirement Density = 500 kg / m3 . -
Partition Coefficients in Mixed Surfactant Systems
Partition coefficients in mixed surfactant systems Application of multicomponent surfactant solutions in separation processes Vom Promotionsausschuss der Technischen Universität Hamburg-Harburg zur Erlangung des akademischen Grades Doktor-Ingenieur genehmigte Dissertation von Tanja Mehling aus Lohr am Main 2013 Gutachter 1. Gutachterin: Prof. Dr.-Ing. Irina Smirnova 2. Gutachterin: Prof. Dr. Gabriele Sadowski Prüfungsausschussvorsitzender Prof. Dr. Raimund Horn Tag der mündlichen Prüfung 20. Dezember 2013 ISBN 978-3-86247-433-2 URN urn:nbn:de:gbv:830-tubdok-12592 Danksagung Diese Arbeit entstand im Rahmen meiner Tätigkeit als wissenschaftliche Mitarbeiterin am Institut für Thermische Verfahrenstechnik an der TU Hamburg-Harburg. Diese Zeit wird mir immer in guter Erinnerung bleiben. Deshalb möchte ich ganz besonders Frau Professor Dr. Irina Smirnova für die unermüdliche Unterstützung danken. Vielen Dank für das entgegengebrachte Vertrauen, die stets offene Tür, die gute Atmosphäre und die angenehme Zusammenarbeit in Erlangen und in Hamburg. Frau Professor Dr. Gabriele Sadowski danke ich für das Interesse an der Arbeit und die Begutachtung der Dissertation, Herrn Professor Horn für die freundliche Übernahme des Prüfungsvorsitzes. Weiterhin geht mein Dank an das Nestlé Research Center, Lausanne, im Besonderen an Herrn Dr. Ulrich Bobe für die ausgezeichnete Zusammenarbeit und der Bereitstellung von LPC. Den Studenten, die im Rahmen ihrer Abschlussarbeit einen wertvollen Beitrag zu dieser Arbeit geleistet haben, möchte ich herzlichst danken. Für den außergewöhnlichen Einsatz und die angenehme Zusammenarbeit bedanke ich mich besonders bei Linda Kloß, Annette Zewuhn, Dierk Claus, Pierre Bräuer, Heike Mushardt, Zaineb Doggaz und Vanya Omaynikova. Für die freundliche Arbeitsatmosphäre, erfrischenden Kaffeepausen und hilfreichen Gespräche am Institut danke ich meinen Kollegen Carlos, Carsten, Christian, Mohammad, Krishan, Pavel, Raman, René und Sucre. -
Chapter 18 Solutions and Their Behavior
Chapter 18 Solutions and Their Behavior 18.1 Properties of Solutions Lesson Objectives The student will: • define a solution. • describe the composition of solutions. • define the terms solute and solvent. • identify the solute and solvent in a solution. • describe the different types of solutions and give examples of each type. • define colloids and suspensions. • explain the differences among solutions, colloids, and suspensions. • list some common examples of colloids. Vocabulary • colloid • solute • solution • solvent • suspension • Tyndall effect Introduction In this chapter, we begin our study of solution chemistry. We all might think that we know what a solution is, listing a drink like tea or soda as an example of a solution. What you might not have realized, however, is that the air or alloys such as brass are all classified as solutions. Why are these classified as solutions? Why wouldn’t milk be classified as a true solution? To answer these questions, we have to learn some specific properties of solutions. Let’s begin with the definition of a solution and look at some of the different types of solutions. www.ck12.org 394 E-Book Page 402 Homogeneous Mixtures A solution is a homogeneous mixture of substances (the prefix “homo-” means “same”), meaning that the properties are the same throughout the solution. Take, for example, the vinegar that is used in cooking. Vinegar is approximately 5% acetic acid in water. This means that every teaspoon of vinegar contains 5% acetic acid and 95% water. When a solution is said to have uniform properties, the definition is referring to properties at the particle level. -
Chapter 4 Solution Theory
SMA5101 Thermodynamics of Materials Ceder 2001 Chapter 4 Solution Theory In the first chapters we dealt primarily with closed systems for which only heat and work is transferred between the system and the environment. In the this chapter, we study the thermodynamics of systems that can also exchange matter with other systems or with the environment, and in particular, systems with more than one component. First we focus on homogeneous systems called solutions. Next we consider heterogeneous systems with emphasis on the equilibrium between different multi-component phases. 4.1 WHAT IS A SOLUTION? A solution in thermodynamics refers to a system with more than one chemical component that is mixed homogeneously at the molecular level. A well-known example of a solution is salt water: The Na+, Cl- and H2O ions are intimately mixed at the atomic level. Many systems can be characterized as a dispersion of one phase within another phase. Although such systems typically contain more than one chemical component, they do not form a solution. Solutions are not limited to liquids: for example air, a mixture of predominantly N2 and O2, forms a vapor solution. Solid solutions such as the solid phase in the Si-Ge system are also common. Figure 4.1. schematically illustrates a binary solid solution and a binary liquid solution at the atomic level. Figure 4.1: (a) The (111) plane of the fcc lattice showing a cut of a binary A-B solid solution whereby A atoms (empty circles) are uniformly mixed with B atoms (filled circles) on the atomic level. -
Ways to Physically Separate a Mixture There Are 2 Types of Mixtures
Mixtures 12 Mixtures Homogenous Compare Heterogeneous compounds and Suspension Mixtures. Colloid Solution Differentiate Solute/Solvent between solutions, suspensions, and colloids Comparing Mixtures and Compounds Mixtures Compounds Made of 2 or more substances Made of 2 or more substances physically combined chemically combined Substances keep their own properties Substances lose their own properties Can be separated by physical means Can be separated only by chemical means Have no definite chemical composition Have a definite chemical composition What method is used to separate mixtures Ways to physically separate a Mixture based on boiling • Distillation – uses boiling point point? • Magnet – uses magnetism What method is used • Centrifuge – uses density to separate mixtures based on density? • Filtering – separates large particles from smaller ones What method is used There are 2 types of mixtures: to separate mixtures (1) Heterogeneous Mixtures: the parts mixed together can still be based on particle size? distinguished from one another...NOT uniform in composition Give examples of a heterogeneous Examples: chicken soup, fruit salad, dirt, sand in water mixture Mixtures 12 (2) Homogenous Mixtures: the parts mixed together cannot be distinguished from one another...completely uniform in composition. Give examples of a homogenous Examples: Air, Kool-aid, Brass, salt water, milk mixture Differentiate Types of Homogenous mixtures between a homogenous 1. Suspensions mixture and a i.e. chocolate milk, muddy water, Italian dressing heterogeneous mixture. They are cloudy (usually a liquid mixed with small solid particles) Identify an example of a suspension. Needs to be shaken or stirred to keep the solids from Will the solid settling particles settle in a suspension? The solids can be filtered out 2.