Phase Diagrams & Thermodynamics


 Mark Stephens
 2 years ago
 Views:
Transcription
1 Phase Diagrams & Thermodynamics A phase diagram is a graphical representation of the equilibrium state of a system using the intensive variables T and i while p is kept constant. The equilibrium may be calculated from thermodynamic data using G for all relevant phases G Solubility of B in pure A Line Compound p const. T const. Solution (e.g. Liquid) Solution with miscibility gap A B B 1 Modeling
2 The Tangent Method Graphical evaluation of equilibria from the G() curves G T, p const. Local equilibrium conditions: phase μ A phase μ A μ B μ B μ A μ A : G ' ' G ' ( ) μ B μ B : G '' '' G ( ) '' G ' ' G + (1 ) ( ) and: T T ; p p ' G '' '' G + (1 ) ( ) '' A B 2 Modeling
3 What do we need for the Calculation? For each phase relevant in the system we need the Gibbs Energy G as a function of the intensive variables p, T, i (analytical epression) The combination of these Gibbs energies defines our thermodynamic model. The minimum of G for the system, and thus the phase equilibria, can be calculated by minimization procedures. Phases: pure condensed substances (elements, compounds) solutions (liquid and solid solutions) nonstoichiometric compounds gas phase (consisting of different gas species i with partial pressure p i ) 3 Modeling
4 Thermodynamic Modeling Literature M. Hillert: Phase Equilibria, Phase Diagrams and Phase Transformations Their Thermodynamic Basis, Cambridge University Press 1998 M Hillert: By modeling we shall understand the selection of some assumptions from which it is possible to calculate the properties of a system 1) Physical models: hypothesis mathematical epression 2) Empirical models: eperimental data mathematical epression 4 Modeling
5 Eample: Simple Empirical Model Consider the representation of G as a power series in T c p But: G G H a + bt + dt c p SER 2 G T ( ) 2dT 2 T Usual course of c p at high temperature T / K This means we need a constant term in c p for a proper description! c p c 2dT... G a + bt + ct lnt + dt Representation generally used in SGTE format. Only valid for high temperatures! 5 Modeling
6 Simple Physical Model: Thermal acancies Consider a pure crystalline solid ( N + N element. The number of possible W arrangements is: N! Nv! )! N: number of atoms N : number of vacancies According to Boltzmann this gives a change in entropy: ΔS k lnw k [( N + N )ln( N + N ) N lnn N lnn ] This may be introduced into the Gibbs Energy: ΔG N N g TΔS g + knt[ln N N + N + N N N ln N + N ] g: energy of formation for one vacancy 6 Modeling
7 Thermal acancies (2) Regard N as internal variable for a Gibbs energy minimization: D G 0 ( ) T, p, N N g + N kt ln N + N Equilibrium fraction of vacancies (for D 0) y D: thermodynamic driving force eq N N + N ep( g kt ) At equilibrium the internal variable (N ) can now be eliminated: ΔG N N g g + knt[ln(1 y knt ln(1 y + knt[ln N eq ) N + N eq ) + N + N N N ln y RT ln[1 ep( 7 Modeling N ln N + N eq g kt ] )] ]
8 Solution Phases Thermodynamic properties have to be modeled as a function of composition ΔG solution phase T, p const. line compound e.g. NaCl, GaAs In fact also shows homogeneity range Depends on the scale! line compound AB 2 solution phase Most liquids Solid solutions nonstoichiometric compounds A B B Two component system (binary) 8 Modeling
9 Ideal Solution G G( p, T, N1, N2,...) G G( p, T, ) (binary system) No difference in the interaction between like and unlike atoms is assumed for the ideal solution : ΔH Δ id id 0 0 A  A A  B B B ΔS id 0 ΔG id 0 ΔS ΔG id id R RT c i 1 c i 1 i ln i i ln i R[ ln + (1 )ln(1 )] RT[ ln + (1 )ln(1 )] As < 1 ln < 0 always stabilizing! 9 Modeling
10 Ideal Solution (2) 0.5 ln + (1 )ln(1 ) lim a0 Δ S id lim Δ a1 lim a0 S id Δ G id lim Δ a1 G id Modeling
11 Regular Solution [Hildebrand 1929]: Interaction between unlike atoms contributes to ΔH. ΔG ε ( 1 ) + RT[ ln + (1 )ln(1 )] Ecess term Ideal term Define Ecess functions of the form Y Y E + Y IDEAL ε < 0 : Additional stabilization from H E ε 0 : Ideal Solution ε > 0 : Interplay between S (stabilization) and H (destabilization) 11 Modeling
12 Regular Solution  Eample ε 12.5 kjmol 1 Critical point [Y.A. Chang, University of Wisconsin] 12 Modeling
13 Regular Solution Eample (2) ε 12.5 kjmol Modeling
14 Regular Solution Eample (3) Resulting phase diagram obtained by the calculation with our regular solution model (ε 12.5 kjmol 1 ) single phase field spinodal curve two phase field 14 Modeling
15 RedlichKister Polynoms Common standard model for solution modeling. Etension of the regular solution model for the modeling of all kinds of asymmetric shapes. I I G B A E Δ ) 1 ( General epression for the binary RedlichKister:... ) ( ) ( B A B A L L L I Δ n k k B A k B A E L G 0 ) ( L is modeled as a function of T e.g.: or higher powers of T bt a L k + 15 Modeling
16 Sublattice Models Nonstoichiometric compounds require composition dependent modeling. Usually they have more than one sublattice. No adequate representation by conventional RedlichKister models! Usual case for crystalline phases: acancies Interstitials Substitutions Occur on different sublattices! Crystal structure and defect mechanisms must be known! Xray diffraction investigations Spectroscopy Diffusion studies, etc 16 Modeling
17 Eample: TiO 2 Sublattice Model Rutile structure type Tetragonal P4 2 /mnm Ti 4+ : 2a (0,0,0) O 2, a 24f (0.3,0.3,0) Sublattice notation: (Ti 4+ ) 1 (O 2,a 2 ) 2 ΔG + y 0 2 y y O 2 a G 2 0 TiO n 2 k 0 k + y a 2 L( T )( y G O 0 Tia 2 2 y + a 2RT ( y 2 ) k O 2 ln y O 2 + y a 2 ln y a 2 ) (y Site fraction) [Waldner and Eriksson, CALPHAD 1999] 17 Modeling
18 Etension to higher order Systems 1) Solutions: The thermodynamic properties of the solution are etrapolated from the thermodynamic properties of the subsystems using different geometrical models. e.g.:  Kohler Model (symmetric)  Muggianu Model (symmetric)  Toop Model (asymmetric) Etrapolation with or without additional interaction parameters 2) Compounds: Up to now it is not possible to predict compound formation Eperiments necessary! Higher order compounds are modeled as line compounds (only temperature dependence) or with suitable sublattice models according to the crystal structure. 18 Modeling
19 Kohler Model A B(AB) C(AC) ΔG + + E ABC A A( AB) A A( AC) B B( BC) B B( AB) C C( AC) C G C( BC) E AB G G E AC E BC A(AC) A(AB) C B Symmetric Etrapolation B(BC) C(BC) 19 Modeling
20 Muggianu Model A B(AB) C(AC) ΔG + + E ABC A A( AB) A A( AC) B B( BC) B B( AB) C C( AC) C G C( BC) E AB G G E AC E BC A(AC) A(AB) C B Symmetric Etrapolation B(BC) C(BC) 20 Modeling
21 Toop Model A(AC) C C(AC) A Asymmetric Component 0.8 B(AB) A(AB) B ΔG + + E ABC A A( AB) A A( AC) B B( BC) B B( AB) C C( AC) C G C( BC) E AB G G E AC E BC Asymmetric Etrapolation B(BC) C(BC) 21 Modeling
22 The CALPHAD Method CALPHAD Calculation of Phase Diagrams Critical assessment and thermodynamic optimization of binary and higher order systems 1) Literature Assessment: evaluation of all available literature sources 2) Modeling of the Gibbs energies G(p,T, i ) for all phases in the system. 3) Optimization of model parameters for best representation of the eperimental data interconsistency of data! Data Sources: Thermodynamics (Calorimetry, EMF, vapor pressure) Phase Diagram Studies (DTA/DSC, Xray diffraction, optical microscopy, SEM/EPMA, ) Other Methods (Diffusion studies, magnetic investigations, ) 22 Modeling
23 Evaluation and selection of input data Thermodynamic modeling of the phases The CALPHAD approach [G. Cacciamani, Genova University] Optimization of model parameters (by error minimization procedures) Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Applications (databases, predictions, simulations, etc.) 23 Modeling
24 The CALPHAD Approach (1) Evaluation and selection of input data Optimisation of model parameters (by error minimisation procedures) Thermodynamic modeling of the phases Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Stoichiometric compounds Ordered solutions Disordered solid solutions Liquids etc. Applications (databases, predictions, simulations, etc.) 24 Modeling
25 The CALPHAD Approach (2) Evaluation and selection of input data Optimisation of model parameters (by error minimisation procedures) Thermodynamic modeling of the phases Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Eperiments (DTA, DSC, calorimetry, EMF, vapor pressure, LOM, SEM, Xray diffraction, etc.) Estimates (periodic properties, chemical criteria, etc.) Theory (abinitio, semiempirical, etc.) Applications (databases, predictions, simulations, etc.) 25 Modeling
26 The CALPHAD Approach (3) Evaluation and selection of input data Thermodynamic modeling of the phases Optimisation of model parameters (by error minimisation procedures) Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Applications (databases, predictions, simulations, etc.) G(P,T, 1,..., i,) Data selection and input Weight assignment Parameter evaluation by nonlinear least squares regression 26 Modeling
27 The CALPHAD Approach (4) Evaluation and selection of input data Thermodynamic modeling of the phases Optimisation of model parameters (by error minimisation procedures) Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Applications (databases, predictions, simulations, etc.) Comparison with input and derived data Compatibility with similar and higher order systems 27 Modeling
28 The CALPHAD Approach (5) Evaluation and selection of input data Thermodynamic modeling of the phases Optimisation of model parameters (by error minimisation procedures) Calculation (phase diagrams, property diagrams, etc.) and Comparison (to the input data) Applications (databases, predictions, simulations, etc.) Database implementation Etrapolation to higher order Materials simulation etc. 28 Modeling
29 The CALPHAD Approach (6) optimized AB optimized AC optimized BC etrapolated ABC a few key data optimized ABC 29 Modeling
30 The CALPHAD Approach (7) optimized ABC optimized ABD optimized ACD optimized BCD etrapolated ABCD a few key data optimized ABCD 30 Modeling
31 Eample: Hypothetical Binaries, Ideal Solution SGTE parameter representation for pure elements (stable and metastable phases) in combination with the ideal solution model. Calculation of hypothetical binary phase diagrams. Program: FazDiaGr by G. Garzeł Data base: 4d and 5d elements of Group 48: Zr, Hf, Nb, Ta, Mo, W, Re, Rh, Ir, Pd, Pt, Ru, Os Phases: Liquid (λ), fcc (α), bcc (β), hcp (ε) 31 Modeling
32 Hypothetical Binaries, Ideal Solution (1) λ β ε α 32 Modeling
33 Hypothetical Binaries, Ideal Solution (2) λ β ε α 33 Modeling
34 Hypothetical Binaries, Ideal Solution (3) λ β ε α 34 Modeling
35 Eample: Modeling using Regular Solutions Binary Phase diagram features modeled with use of the regular solution model Cigar shape of the solid/liquid phase boundaries Maimum congruent melting of the solid phase Minimum congruent melting of the solid phase Peritectic phase diagram Eutectic phase diagram T S m A m A 800 S m B K, 20 T m B J / 1000 K mol K Regular solution parameters ε l and ε s are varied 35 Modeling
36 1  Liquidus and Solidus Curves 1000 ε l ε s T(K) 900 ε l s ε 5kJ Solid Liquid 850 ε l s ε 15kJ Mole Fraction of B 36 Modeling
37 2  Maimum and Minimum 1100 ε l s ε 0 10kJ / mol Liquid 1000 T(K) 900 ε l s ε 0 0 ε l s ε 12kJ / mol 700 Solid 10kJ / mol Mole Fraction of B ε l s ε 37 Modeling
38 3  Peritectic Phase Diagram ε l ε s 15 kj Liquid 900 T(K) Solid ε l s ε 12kJ / mol Solid+Solid Mole fraction of B 38 Modeling
39 4  Eutectic Phase Diagram ε l s ε 0 15kJ / mol Liquid T(K) Solid ε l s ε 20kJ / mol 25kJ / mol ε l s ε 0 10kJ / mol Solid+Solid Mole fraction of B 39 Modeling
40 5  Monotectic Phase Diagram ε l s ε 17.5kJ 13.5kJ / mol / mol Liquid 1000 Liq+liq T(K) Liquid+Solid Solid Solid+Solid Mole fraction of B 40 Modeling
41 6  Syntectic Phase Diagram ε l s ε 25kJ / mol 10kJ / mol Liquid 1200 Liquid+liquid T(K) 900 Liquid+Solid Solid 600 Solid+Solid Mole fraction of B 41 Modeling
42 7 Monotectic + Peritectic Phase Diagram 1500 ε l s ε 20kJ 20kJ / mol / mol Liquid 1200 Liquid+liquid T(K) 900 Liquid+Solid Solid 600 Solid Solid+Solid Mole fraction of B 42 Modeling
43 Models: Eample: Modeling of binary InNi CALPHAD assessment by Waldner and Ipser L, (Ni): RedlichKister solution models δ: (Ni,a) 1 (In,Ni) 1 sublattice model ξ, ξ : (Ni,a) 1 (Ni) 1 (In,Ni) 1 sublattice models Ni 3 In, Ni 2 In, NiIn, Ni 2 In 3, Ni 3 In 7 : Stoichiometric [Massalski s Phase Diagram Compilation] 43 Modeling
44 Modeling of binary InNi (1) Data Sources: Phase diagram: mainly 2 papers ( + older literature) apor pressure data: 3 papers EMF measurements: 5 papers Calorimetry: 3 papers Crystal structure: various literature on defect mechanisms of the structure type Used as input for the optimization procedure 44 Modeling
45 Modeling of binary InNi (2) Calorimetric data 45 Modeling
46 Modeling of binary InNi (3) apor pressure data 46 Modeling
47 Modeling of binary InNi (4) Pressures over Ni 2 In from EMF and Knudsen sources 47 Modeling
48 Modeling of binary InNi (5) Enthalpies from EMF and Calorimetric sources 48 Modeling
49 Modeling of binary InNi (6) Fit with phase diagram data 49 Modeling
Chapter 8. Phase Diagrams
Phase Diagrams A phase in a material is a region that differ in its microstructure and or composition from another region Al Al 2 CuMg H 2 O(solid, ice) in H 2 O (liquid) 2 phases homogeneous in crystal
More informationELECD Principles of materials science Thermodynamics and diffusion. ELECD Principles of materials science
Thu 3.3 Mon 7.3 ELECD8710  Principles of materials science Thermodynamics and diffusion Thu 10.3 Exercise 5 Mon 14.3 Thu 17.3 Exercise 6 Mon 21.3 Thermodynamics  Principles (T,xi) equilibrium diagrams
More informationPhase Equilibria & Phase Diagrams
Phase Equilibria & Phase Diagrams Week7 Material Sciences and Engineering MatE271 1 Motivation Phase diagram (Ch 9) Temperature Time Kinematics (Ch 10) New structure, concentration (mixing level) (at what
More informationThe ClausiusClapeyron Equation:
Chapter 10 Solid Solutions and Phase Equilibrium What is a phase? Phase Diagram Basics A phase diagram represents what phases are present at a given pressure, temperature and composition. Virtual maps
More informationμ α =μ β = μ γ = =μ ω μ α =μ β =μ γ = =μ ω Thus for c components, the number of additional constraints is c(p 1) ( ) ( )
Phase Diagrams 1 Gibbs Phase Rule The Gibbs phase rule describes the degrees of freedom available to describe a particular system with various phases and substances. To derive the phase rule, let us begin
More informationAP CHEMISTRY 2007 SCORING GUIDELINES. Question 2
AP CHEMISTRY 2007 SCORING GUIDELINES Question 2 N 2 (g) + 3 F 2 (g) 2 NF 3 (g) ΔH 298 = 264 kj mol 1 ; ΔS 298 = 278 J K 1 mol 1 The following questions relate to the synthesis reaction represented by the
More informationBINARY SYSTEMS. Definition of Composition: Atomic (molar) fraction. Atomic percent. Mass fraction. Mass percent (weight percent)
BINARY SYSTEMS Definition of Composition: Atomic (molar) fraction Atomic percent Mass fraction Mass percent (weight percent) na =, x i n = A i i i Weight percent mainly in industry! x at % A = x 100 A
More informationFinal Exam CHM 3410, Dr. Mebel, Fall 2005
Final Exam CHM 3410, Dr. Mebel, Fall 2005 1. At 31.2 C, pure propane and nbutane have vapor pressures of 1200 and 200 Torr, respectively. (a) Calculate the mole fraction of propane in the liquid mixture
More information1 Exercise 5.33b pg 204
In this solution set, an underline is used to show the last significant digit of numbers. For instance in x = 2.51693 the 2,5,1, and 6 are all significant. Digits to the right of the underlined digit,
More informationMean Field Flory Huggins Lattice Theory
Mean Field Flory Huggins Lattice Theory Mean field: the interactions between molecules are assumed to be due to the interaction of a given molecule and an average field due to all the other molecules in
More informationLN 10. 3.091 Introduction to Solid State Chemistry. Lecture Notes No. 10 PHASE EQUILIBRIA AND PHASE DIAGRAMS
3.091 Introduction to Solid State Chemistry Lecture Notes No. 10 PHASE EQUILIBRIA AND PHASE DIAGRAMS * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Sources
More informationChapter 5: Diffusion. 5.1 SteadyState Diffusion
: Diffusion Diffusion: the movement of particles in a solid from an area of high concentration to an area of low concentration, resulting in the uniform distribution of the substance Diffusion is process
More informationThermodynamics. Chapter 13 Phase Diagrams. NC State University
Thermodynamics Chapter 13 Phase Diagrams NC State University Pressure (atm) Definition of a phase diagram A phase diagram is a representation of the states of matter, solid, liquid, or gas as a function
More informationThermodynamics of Mixing
Thermodynamics of Mixing Dependence of Gibbs energy on mixture composition is G = n A µ A + n B µ B and at constant T and p, systems tend towards a lower Gibbs energy The simplest example of mixing: What
More informationVYSOKÁ ŠKOLA BÁŇSKÁ TECHNICAL UNIVERSITY OF OSTRAVA COMPUTER SIMULATION AND MODELLING IN MATERIALS ENGINEERING. Study Support
VYSOKÁ ŠKOLA BÁŇSKÁ TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF METALLURGY AND MATERIALS ENGINEERING COMPUTER SIMULATION AND MODELLING IN MATERIALS ENGINEERING Study Support Jaromír Drápala, Vlastimil Vodárek,
More informationGibbs Free Energy and Chemical Potential. NC State University
Chemistry 433 Lecture 14 Gibbs Free Energy and Chemical Potential NC State University The internal energy expressed in terms of its natural variables We can use the combination of the first and second
More informationLecture 6 Application of Thermodynamics in Phase Diagrams. Today s Topics
Lecture 6 Application of Thermodynamics in Phase Diagrams A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics The phase diagrams and its applications The structure of phase diagrams
More informationBinary Solutions. Reading: Chapter 1.3 of Porter and Easterling, Chapters 9.5, 9.6, 9.9, 9.10 of Gaskell
inary Solutions Composition as a thermodynamic variable ibbs free energy of binary solutions Entropy of formation and ibbs free energy of an ideal solution Regular solutions: Heat of formation of a solution
More informationThermodynamic database of the phase diagrams in copper base alloy systems
Journal of Physics and Chemistry of Solids 66 (2005) 256 260 www.elsevier.com/locate/jpcs Thermodynamic database of the phase diagrams in copper base alloy systems C.P. Wang a, X.J. Liu b, M. Jiang b,
More informationPhase Transformations
Vysoká škola báňská Technická univerzita Ostrava Phase Transformations Didactic Text Vlastimil Vodárek Ostrava 2013 Review: Prof. Dr. Ing. Jaroslav Sojka Description: Phase Transformations Author: Vlastimil
More informationIntroduction to Materials Science, Chapter 9, Phase Diagrams. Phase Diagrams. University of Tennessee, Dept. of Materials Science and Engineering 1
Phase Diagrams University of Tennessee, Dept. of Materials Science and Engineering 1 Chapter Outline: Phase Diagrams Microstructure and Phase Transformations in Multicomponent Systems Definitions and basic
More informationThe first law: transformation of energy into heat and work. Chemical reactions can be used to provide heat and for doing work.
The first law: transformation of energy into heat and work Chemical reactions can be used to provide heat and for doing work. Compare fuel value of different compounds. What drives these reactions to proceed
More informationLecture 3: Models of Solutions
Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP4, Thermodynamics and Phase Diagrams, H. K. D. H. Bhadeshia Lecture 3: Models of Solutions List of Symbols Symbol G M
More informationPressure/composition phase diagram There are 2 main types of composition diagrams pressure and temperature. This is an example of how the total vapor
Pressure/composition phase diagram There are 2 main types of composition diagrams pressure and temperature. This is an example of how the total vapor pressure changes for an ideal solution. Pressure/composition
More informationSimple Mixtures. Atkins 7th: Sections ; Atkins 8th: The Properties of Solutions. Liquid Mixtures
The Properties of Solutions Simple Mixtures Atkins 7th: Sections 7.47.5; Atkins 8th: 5.45.5 Liquid Mixtures Colligative Properties Boiling point elevation Freezing point depression Solubility Osmosis
More informationThermodynamics: First Law, Calorimetry, Enthalpy. Calorimetry. Calorimetry: constant volume. Monday, January 23 CHEM 102H T.
Thermodynamics: First Law, Calorimetry, Enthalpy Monday, January 23 CHEM 102H T. Hughbanks Calorimetry Reactions are usually done at either constant V (in a closed container) or constant P (open to the
More informationTERNARY SYSTEMS. x 1 + x 2 + x 3 = 1 in the same way: h 1 + h 2 + h 3 = h triangle. Concentration given in Gibbs Triangle. h triangle. h 2. h 3.
TERNARY SYSTEMS Concentration given in Gibbs Triangle x 1 h triangle h 2 h 1 x 3 h 3 x 2 x 3 x 1 x 1 + x 2 + x 3 = 1 in the same way: h 1 + h 2 + h 3 = h triangle 270121 VO Phasendiagramme Ternäre Systeme
More informationThermoCalc Software. Data Organization and Knowledge Discovery. Paul Mason ThermoCalc Software, Inc. ThermoChemistry to Phase Diagrams and More
ThermoCalc Software Data Organization and Knowledge Discovery ThermoChemistry to Phase Diagrams and More Paul Mason ThermoCalc Software, Inc. http://www.thermocalc.com Tel: (724) 731 0074 Email: paul@thermocalc.com
More informationH 2 (g) + ½ O 2 (g) H 2 O(l) H o f [NO(g)] = 90.2 kj/mol; H o f [H 2 O(g)] = kj/mol H o f [NH 3 (g)] = kj/mol; H o f [O 2 (g)] =?
Chapter 16 Thermodynamics GCC CHM152 Thermodynamics You are responsible for Thermo concepts from CHM 151. You may want to review Chapter 8, specifically sections 2, 5, 6, 7, 9, and 10 (except work ). Thermodynamics:
More informationReading: Moore chapter 18, sections 18.618.11 Questions for Review and Thought: 62, 69, 71, 73, 78, 83, 99, 102.
Thermodynamics 2: Gibbs Free Energy and Equilibrium Reading: Moore chapter 18, sections 18.618.11 Questions for Review and Thought: 62, 69, 71, 73, 78, 83, 99, 102. Key Concepts and skills: definitions
More informationPhase. Gibbs Phase rule
Phase diagrams Phase A phase can be defined as a physically distinct and chemically homogeneous portion of a system that has a particular chemical composition and structure. Water in liquid or vapor state
More informationAP Practice Questions
1) AP Practice Questions The tables above contain information for determining thermodynamic properties of the reaction below. C 2 H 5 Cl(g) + Cl 2 (g) C 2 H 4 Cl 2 (g) + HCl(g) (a) Calculate ΔH for
More information4. Thermodynamics of Polymer Blends
4. Thermodynamics of Polymer Blends Polymeric materials find growing applications in various fields of everyday life because they offer a wide range of application relevant properties. Blending of polymers
More informationLecture 1: Physical Equilibria The Temperature Dependence of Vapor Pressure
Lecture 1: Physical Equilibria The Temperature Dependence of Vapor Pressure Our first foray into equilibria is to examine phenomena associated with two phases of matter achieving equilibrium in which the
More informationThermodynamics explores the connection between energy and the EXTENT of a reaction but does not give information about reaction rates (Kinetics).
Thermodynamics explores the connection between energy and the EXTENT of a reaction but does not give information about reaction rates (Kinetics). Rates of chemical reactions are controlled by activation
More informationEach grain is a single crystal with a specific orientation. Imperfections
Crystal Structure / Imperfections Almost all materials crystallize when they solidify; i.e., the atoms are arranged in an ordered, repeating, 3dimensional pattern. These structures are called crystals
More informationLecture 5: Diffusion Coefficient (Diffusivity)
Lecture 5: Diffusion Coefficient (Diffusivity) Today s topics Understand the general physical meaning of diffusion coefficient. What is chemical diffusion coefficient (D C ) and tracer diffusion coefficient
More informationLecture 19: Eutectoid Transformation in Steels: a typical case of Cellular
Lecture 19: Eutectoid Transformation in Steels: a typical case of Cellular Precipitation Today s topics Understanding of Cellular transformation (or precipitation): when applied to phase transformation
More informationSOLIDIFICATION. (a)formation of stable nuclei. Growth of a stable nucleus. (c) Grain structure
SOLIDIFICATION Most metals are melted and then cast into semifinished or finished shape. Solidification of a metal can be divided into the following steps: Formation of a stable nucleus Growth of a stable
More informationThermal Analysis TGA / DTA. Linda Fröberg
Thermal Analysis TGA / DTA Linda Fröberg Outline Definitions What is thermal analysis? Instrumentation & origin of the TGADTA signal. TGA DTA Basics and applications Phase diagrams & Thermal analysis
More informationPhase Transformations in Metals and Alloys
Phase Transformations in Metals and Alloys THIRD EDITION DAVID A. PORTER, KENNETH E. EASTERLING, and MOHAMED Y. SHERIF ( г йс) CRC Press ^ ^ ) Taylor & Francis Group Boca Raton London New York CRC Press
More informationReview of Chemical Equilibrium Introduction
Review of Chemical Equilibrium Introduction Copyright c 2016 by Nob Hill Publishing, LLC This chapter is a review of the equilibrium state of a system that can undergo chemical reaction Operating reactors
More informationRate of Reaction and the Collision Theory. Factors that Affect the Rate of a Chemical Reaction
Chemical Kinetics and Thermodynamics Chemical Kinetics concerned with: 1. Rates of Chemical Reactions # of moles of reactant used up or product formed Unit time Or 2. Reaction Mechanisms Rate of Reaction
More information1 Phase Equilibria [1]
1 Phase Equilibria [1] Vaporliquid equilibrium VLE) is the state of coexistence between liquid and vapor phases. For a one component system, this is easily visualized, as shown in Figure 1. As the number
More informationImperfections in atomic arrangements
MME131: Lecture 8 Imperfections in atomic arrangements Part 1: 0D Defects A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Occurrence and importance of crystal defects Classification
More informationThermodynamics and Kinetics. Lecture 14 Properties of Mixtures Raoult s Law Henry s Law Activity NC State University
Thermodynamics and Kinetics Lecture 14 Properties of Mixtures Raoult s Law Henry s Law Activity NC State University Measures of concentration There are three measures of concentration: molar concentration
More informationStatistical Physics Exam
Statistical Physics Exam 23rd April 24 Name Student Number Problem Problem 2 Problem 3 Problem 4 Total Percentage Mark Useful constants gas constant R Boltzmann constant k B Avogadro number N A speed of
More informationChapter 20. Thermodynamics p. 811 842. Spontaneity. What have we learned about spontaneity during this course?
Chapter 20 p. 811 842 Spontaneous process: Ex. Nonspontaneous process: Ex. Spontaneity What have we learned about spontaneity during this course? 1) Q vs. K? 2) So.. Spontaneous process occurs when a system
More informationKinetics of Phase Transformations: Nucleation & Growth
Kinetics of Phase Transformations: Nucleation & Growth Radhika Barua Department of Chemical Engineering Northeastern University Boston, MA USA Thermodynamics of Phase Transformation Northeastern University
More informationBomb Calorimetry. Example 4. Energy and Enthalpy
Bomb Calorimetry constant volume often used for combustion reactions heat released by reaction is absorbed by calorimeter contents need heat capacity of calorimeter q cal = q rxn = q bomb + q water Example
More informationChapter 17 Thermodynamics: Directionality of Chemical Reactions
Reactant & ProductFavored Processes John W. Moore Conrad L. Stanitski Peter C. Jurs http://academic.cengage.com/chemistry/moore Chapter 17 hermodynamics: Directionality of Chemical Reactions Why are
More informationMaterials Science and Engineering Department MSE , Sample Test #1, Spring 2010
Materials Science and Engineering Department MSE 200001, Sample Test #1, Spring 2010 ID number First letter of your last name: Name: No notes, books, or information stored in calculator memories may be
More informationLecture 4: Thermodynamics of Diffusion: Spinodals
Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP6, Kinetics and Microstructure Modelling, H. K. D. H. Bhadeshia Lecture 4: Thermodynamics of Diffusion: Spinodals Fick
More informationExpt. 5: Binary Phase Diagram CHEM 366 V1. Binary SolidLiquid Phase Diagram
Expt. 5: Binary Phase Diagram CHEM 366 V1 Introduction Binary SolidLiquid Phase Diagram The substances that we encounter in the material world are hardly ever pure chemical compounds but rather mixtures
More informationChemistry 433. The Third Law of Thermodynamics. Residual Entropy. CO: an Imperfect Crystal. Question. Question. Lecture 12 The Third Law
Chemistry 433 Lecture 12 he hird Law he hird Law of hermodynamics he third law of thermodynamics states that every substance has a positive entropy, but at zero Kelvin the entropy is zero for a perfectly
More informationThe Equipartition Theorem
The Equipartition Theorem Degrees of freedom are associated with the kinetic energy of translations, rotation, vibration and the potential energy of vibrations. A result from classical statistical mechanics
More informationReading. Spontaneity. Monday, January 30 CHEM 102H T. Hughbanks
Thermo Notes #3 Entropy and 2nd Law of Thermodynamics Monday, January 30 CHEM 102H T. Hughbanks Reading You should reading Chapter 7. Some of this material is quite challenging, be sure to read this material
More informationa mixture each Processing methods 1. Singlestage process (batchwise or continuously) 2. Multiplestage process (batchwise or continuously) process.
Introduction to Separation Processes What are separation processes? those operations which transform a mixture of substances into two or more products which differ from each other in composition. Two important
More informationChapter 12 Solutions
Chapter 12 Solutions 12.1 Ideal solutions Solutions are arguably the most important kind of system studied by chemical engineers, whether in large chemical processing or cellularlevel molecular phenomena.
More informationCh. 4: Imperfections in Solids Part 1. Dr. Feras Fraige
Ch. 4: Imperfections in Solids Part 1 Dr. Feras Fraige Outline Defects in Solids 0D, Point defects vacancies Interstitials impurities, weight and atomic composition 1D, Dislocations edge screw 2D, Grain
More informationChapter 15 Chemical Equilibrium
Chapter 15 Chemical Equilibrium Chemical reactions can reach a state of dynamic equilibrium. Similar to the equilibrium states reached in evaporation of a liquid in a closed container or the dissolution
More informationAdvanced Higher Chemistry. THERMODYNAMICS (Reaction Feasibility) Learning Outcomes Questions & Answers
Advanced Higher Chemistry Unit 2  Chemical Reactions THERMODYNAMICS (Reaction Feasibility) Learning Outcomes Questions & Answers KHS Chemistry Nov 2006 page 1 4. THERMODYNAMICS (Reaction Feasibility)
More informationModule 5 : Electrochemistry Lecture 22 : Free energy and EMF
Module 5 : Electrochemistry Lecture 22 : Free energy and EMF Objectives After studying this Lecture you will be able to Distinguish between electrolytic cells and galvanic cells. Write the cell representation
More informationCrystal Structures of Interest
rystal Structures of Interest Elemental solids: Facecentered cubic (fcc) Hexagonal closepacked (hcp) odycentered cubic (bcc) Diamond cubic (dc) inary compounds Fccbased (u 3 u,nal, ßZnS) Hcpbased
More informationvap H = RT 1T 2 = 30.850 kj mol 1 100 kpa = 341 K
Thermodynamics: Examples for chapter 6. 1. The boiling point of hexane at 1 atm is 68.7 C. What is the boiling point at 1 bar? The vapor pressure of hexane at 49.6 C is 53.32 kpa. Assume that the vapor
More information1. the same as E. correct. 2. less than E. 3. unrelated to E.
Version PREVIEW Exam 3 JONSON (53140) 1 This printout should have 40 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. LDE Carbon Allotropes
More informationPeriodic Table of the Elements
Periodic Table of the Elements 1A 8A 1 18 1 2 H 2A 3A 4A 5A 6A 7A He 1.0079 2 13 14 15 16 17 4.0026 3 4 5 6 7 8 9 10 Li Be B C N O F Ne 6.941 9.0122 10.811 12.011 14.0067 15.9994 18.9984 20.1797 11 12
More informationChapter 14. CHEMICAL EQUILIBRIUM
Chapter 14. CHEMICAL EQUILIBRIUM 14.1 THE CONCEPT OF EQUILIBRIUM AND THE EQUILIBRIUM CONSTANT Many chemical reactions do not go to completion but instead attain a state of chemical equilibrium. Chemical
More informationTest Review # 9. Chemistry R: Form TR9.13A
Chemistry R: Form TR9.13A TEST 9 REVIEW Name Date Period Test Review # 9 Collision theory. In order for a reaction to occur, particles of the reactant must collide. Not all collisions cause reactions.
More informationThermodynamics and Equilibrium
Chapter 19 Thermodynamics and Equilibrium Concept Check 19.1 You have a sample of 1.0 mg of solid iodine at room temperature. Later, you notice that the iodine has sublimed (passed into the vapor state).
More information1 Exercise 5.5b pg 201
In this solution set, an underline is used to show the last significant digit of numbers. For instance in x 2.51693 the 2,5,1, and 6 are all significant. Digits to the right of the underlined digit, the
More informationChemical Vapor Deposition
Chemical Vapor Deposition Physical Vapor Deposition (PVD) So far we have seen deposition techniques that physically transport material from a condensed phase source to a substrate. The material to be deposited
More informationDetermination of Molecular Weight by Freezing Point Depression
Determination of Molecular Weight by Freezing Point Depression Freezing point depression is a kind of colligative properties as treated in high school chemistry course. Normally used alcohol or mercury
More informationChapter 5. Thermochemistry
Chapter 5. Thermochemistry THERMODYNAMICS  study of energy and its transformations Thermochemistry  study of energy changes associated with chemical reactions Energy  capacity to do work or to transfer
More informationThermodynamics Answers to Tutorial # 1
Thermodynamics Answers to Tutorial # 1 1. (I) Work done in free expansion is Zero as P ex = 0 (II) Irreversible expansion against constant external pressure w = P ex (V 2 V 1 ) V 2 = nrt P 2 V 1 = nrt
More information6. 2. Unit 6: Physical chemistry of spectroscopy, surfaces and chemical and phase equilibria
6. 2 Phase equilibria Many industrial processes involve several phases in equilibrium gases, liquids, solids and even different crystalline forms of the solid state. Predicting the number of phases present
More informationLecture 3: Introduction to Diffusion
Materials Science & Metallurgy Master of Philosophy, Materials Modelling, Course MP6, Kinetics and Microstructure Modelling, H. K. D. H. Bhadeshia Lecture 3: Introduction to Diffusion Mass transport in
More informationMineral Stability Diagrams and Chemical Weathering of Feldspars
Mineral Stability Diagrams and Chemical Weathering of Feldspars Albite Jadeite Quartz dδg = ΔVdP  ΔSdT and G, S, V values for albite, jadeite and quartz to calculate the conditions for which ΔG of the
More informationAnswers: Given: No. [COCl 2 ] = K c [CO][Cl 2 ], but there are many possible values for [CO]=[Cl 2 ]
Chemical Equilibrium What are the concentrations of reactants and products at equilibrium? How do changes in pressure, volume, temperature, concentration and the use of catalysts affect the equilibrium
More informationGas phase transport reactions. Transport reaction A(s) + B(g) = AB(g)
Gas phase transport reactions CT CVT CTR Chemical Transport Chemical Vapour Transport Chemical Transport Reaction Fast stoff A Gassfase Fast stoff A Used to: Purify materials Grow single crystals Increase
More informationChem 115 POGIL Worksheet  Week 4 Moles & Stoichiometry
Chem 115 POGIL Worksheet  Week 4 Moles & Stoichiometry Why? Chemists are concerned with mass relationships in chemical reactions, usually run on a macroscopic scale (grams, kilograms, etc.). To deal with
More informationThermochemistry. Thermochemistry 1/25/2010. Reading: Chapter 5 (omit 5.8) As you read ask yourself
Thermochemistry Reading: Chapter 5 (omit 5.8) As you read ask yourself What is meant by the terms system and surroundings? How are they related to each other? How does energy get transferred between them?
More informationIn order to solve this problem it is first necessary to use Equation 5.5: x 2 Dt. = 1 erf. = 1.30, and x = 2 mm = 2 103 m. Thus,
5.3 (a) Compare interstitial and vacancy atomic mechanisms for diffusion. (b) Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion. Solution (a) With vacancy diffusion,
More informationDefects Introduction. Bonding + Structure + Defects. Properties
Defects Introduction Bonding + Structure + Defects Properties The processing determines the defects Composition Bonding type Structure of Crystalline Processing factors Defects Microstructure Types of
More informationChem 420/523 Chemical Thermodynamics Homework Assignment # 6
Chem 420/523 Chemical hermodynamics Homework Assignment # 6 1. * Solid monoclinic sulfur (S α ) spontaneously converts to solid rhombic sulfur (S β ) at 298.15 K and 0.101 MPa pressure. For the conversion
More informationThermochemistry. r2 d:\files\courses\111020\99heat&thermorans.doc. Ron Robertson
Thermochemistry r2 d:\files\courses\111020\99heat&thermorans.doc Ron Robertson I. What is Energy? A. Energy is a property of matter that allows work to be done B. Potential and Kinetic Potential energy
More informationMajor chemistry laws. Mole and Avogadro s number. Calculating concentrations.
Major chemistry laws. Mole and Avogadro s number. Calculating concentrations. Major chemistry laws Avogadro's Law Equal volumes of gases under identical temperature and pressure conditions will contain
More informationVaporLiquid Equilibria
31 Introduction to Chemical Engineering Calculations Lecture 7. VaporLiquid Equilibria Vapor and Gas Vapor A substance that is below its critical temperature. Gas A substance that is above its critical
More informationRange of Competencies
CHEMISTRY Content Domain Range of Competencies l. Nature of Science 0001 0003 18% ll. Matter and Atomic Structure 0004 0006 18% lll. Energy and Chemical Bonding 0007 0010 23% lv. Chemical Reactions 0011
More information3.091 OCW Scholar Fall 2010 Final Exam  Solutions Key. Prof. Donald R. Sadoway, Instructor
.091 OCW Scholar Fall 2010 Final Exam  Solutions Key Prof. Donald R. Sadoway, Instructor .091 Fall Term 2010 Final Exam page 2 Problem #1 (20 points) Answer the following questions about the hydrogen
More informationGibbs Energy Modeling of Binary and Ternary Molten Nitrate Salt Systems
Lehigh University Lehigh Preserve Theses and Dissertations 2012 Gibbs Energy Modeling of Binary and Ternary Molten Nitrate Salt Systems Tucker Elliott Lehigh University Follow this and additional works
More informationStandard Free Energies of Formation at 298 K. Average Bond Dissociation Energies at 298 K
1 Thermodynamics There always seems to be at least one free response question that involves thermodynamics. These types of question also show up in the multiple choice questions. G, S, and H. Know what
More informationCrystallization and energy relations between states of matter
Crystallization and energy relations between states of matter This text is meant as background information about how undercooling happens, and how the latent heat of crystallization has to be released
More informationk 2f, k 2r C 2 H 5 + H C 2 H 6
hemical Engineering HE 33 F pplied Reaction Kinetics Fall 04 Problem Set 4 Solution Problem. The following elementary steps are proposed for a gas phase reaction: Elementary Steps Rate constants H H f,
More informationChapter 7: Stoichiometry  Mass Relations in Chemical Reactions
Chapter 7: Stoichiometry  Mass Relations in Chemical Reactions How do we balance chemical equations? How can we used balanced chemical equations to relate the quantities of substances consumed and produced
More informationFUNDAMENTALS OF ENGINEERING THERMODYNAMICS
FUNDAMENTALS OF ENGINEERING THERMODYNAMICS System: Quantity of matter (constant mass) or region in space (constant volume) chosen for study. Closed system: Can exchange energy but not mass; mass is constant
More informationExploring Creation With Chemistry Table of Contents
Exploring Creation With Chemistry Table of Contents MODULE #1: Measurement and Units...1 Introduction... 1 Experiment 1.1: Air Has Mass... 1 Experiment 1.2: Air Takes Up Space... 2 Units of Measurement...
More informationChapter 16 Review Packet
Chapter 16 Review Packet AP Chemistry Chapter 16 Practice Multiple Choice Portion 1. For which process is ΔS negative? Note: ΔS = S final S initial therefore, if ΔS is positive, S final > S initial if
More informationFORMA is EXAM I, VERSION 1 (v1) Name
FORMA is EXAM I, VERSION 1 (v1) Name 1. DO NOT TURN THIS PAGE UNTIL DIRECTED TO DO SO. 2. These tests are machine graded; therefore, be sure to use a No. 1 or 2 pencil for marking the answer sheets. 3.
More informationMr. Bracken. Multiple Choice Review: Thermochemistry
Mr. Bracken AP Chemistry Name Period Multiple Choice Review: Thermochemistry 1. If this has a negative value for a process, then the process occurs spontaneously. 2. This is a measure of how the disorder
More information