Lecture 3 Binary Phase Diagrams - MIT OpenCourseWare
Mapping Stability: BinaryPhase Diagrams22.14 – Intro to Nuclear MaterialsFebruary 19 & 24, 2015Images from Engineering Materials Science,Milton Ohring unless otherwise noted22.14 – Intro to Nuclear MaterialsSlide 1
Major Steps Phase diagramsReading phase diagramsThermodynamicsFree energyFree energy diagramsConstructing phase diagrams from freeenergy diagrams22.14 – Intro to Nuclear MaterialsSlide 2
Phase Diagram: ExampleLiquid regionTwo-phaseregionsα regionβ region Elsevier, Inc. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 3
hase Diagram Microstructur Elsevier, Inc. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide
Phase Separation in Real LifeImage removed due to copyright restrictions. See Fig. 1 from l for further details.22.14 – Intro to Nuclear MaterialsSlide 5
Examples: Complete SolubilitySource: ASM Handbook, Volume 3: Alloy Phase Diagrams. Reprinted withpermission of ASM International .Binary phase diagrams from ASM Handbooks, Vol. 3 (available at vera.mit.edu)22.14 – Intro to Nuclear MaterialsSlide 6
Examples: Miscibility GapSource: ASM Handbook, Volume 3: Alloy Phase Diagrams. Reprinted withpermission of ASM International .22.14 – Intro to Nuclear MaterialsSlide 7
Examples: IntermetallicsSource: ASM Handbook, Volume 3: Alloy Phase Diagrams. Reprinted withpermission of ASM International .22.14 – Intro to Nuclear MaterialsSlide 8
Example Phase DiagramsSource: ASM Handbook, Volume 3: Alloy Phase Diagrams. Reprinted withpermission of ASM International .22.14 – Intro to Nuclear MaterialsSlide 9
Examples: Eutectic, Everything!Source: ASM Handbook, Volume 3: Alloy Phase Diagrams. Reprinted withpermission of ASM International .22.14 – Intro to Nuclear MaterialsSlide 10
Fe-C Phase DiagramBasis for steelmakingMost important one toremember &understand! Elsevier, Inc. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 11
Fe-C Phase DiagramA1: Temperature atwhich phasetransformationfrom α-γ begins Elsevier, Inc. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsA3: Temperature atwhich it endsSlide 12
Fe-C Phase DiagramCompositiondetermines endingmicrostructureMicrostructuredetermines steelproperties Elsevier, Inc. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 13
Reading Phase Diagrams Elsevier, Inc. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 14
Reading Phase Diagrams: TheLever RuleSource: ASM Handbook, Volume 3: Alloy Phase Diagrams. Reprinted withpermission of ASM International .22.14 – Intro to Nuclear MaterialsSlide 15
Reading Phase Diagrams: TheLever Rule𝐶𝐶0 ��𝑂 𝜷𝑪𝑪𝜶𝜶𝐶𝐶𝛼𝛼 ��𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑜𝑜𝑜𝑜𝛼𝛼𝐶𝐶𝛽𝛽 ��𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑜𝑜𝑜𝑜𝛽𝛽𝑓𝑓𝛼𝛼 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 ��𝑓𝑓𝑓 𝑜𝑜𝑜𝑜𝛼𝛼𝐶𝐶𝛽𝛽 𝐶𝐶0 𝐶𝐶𝛽𝛽 ��𝑪𝜷𝜷Source: ASM Handbook, Volume 3: Alloy Phase Diagrams. Reprinted withpermission of ASM International .22.14 – Intro to Nuclear Materials𝑓𝑓𝛽𝛽 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 ��𝑓𝑓𝑓 𝑜𝑜𝑜𝑜𝛽𝛽𝐶𝐶0 𝐶𝐶𝛼𝛼 𝐶𝐶𝛽𝛽 𝐶𝐶𝛼𝛼Slide 16
Reading Phase Diagrams: TheLever Rule𝐶𝐶0 𝑓𝑓𝛼𝛼 𝐶𝐶𝛼𝛼 1 𝑓𝑓𝛼𝛼 .14 – Intro to Nuclear MaterialsHow much of each phaseexists at the ���𝑪𝑪𝜷𝜷What are the compositionsof each phase?Slide 17
Reading Phase Diagrams Elsevier, Inc. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 18
Reading Phase Diagrams Elsevier, Inc. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 19
Reading Phase Diagrams Elsevier, Inc. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 20
Thermodynamics ReviewGibbs Free EnergyVolume22.14 – Intro to Nuclear MaterialsPressureTemperatureEntropyInternal Energy?Slide 21
Free EnergyEach component i has a tabulated, specific Gibbs free energy (ΔGi)– Lower ΔGi indicates higher stabilityCourtesy of UC Davis ChemWiki. License: CC by-nc-sa.http://chemwiki.ucdavis.edu/Analytical Chemistry/Electrochemistry/Electrochemistry and Thermodynamics22.14 – Intro to Nuclear MaterialsSlide 22
Free Energy of MixturesTwo parts:– Atomic (mole) fractions of free energies– Free energy from mixingMole fraction of component AGibbs free energy of component B22.14 – Intro to Nuclear MaterialsSlide 23
Obtaining ΔGmix22.14 – Intro to Nuclear MaterialsSlide 24
Obtaining ΔHmixLet's take a system of atoms (A & B) which totalsone mole (Nav), with mole fractions XA & XB:Energy of an A-A bond EA-AEnergy of an B-B bond EB-BEA-AEnergy of an A-B bond EA-B22.14 – Intro to Nuclear MaterialsSlide 25
Obtaining ΔHmixOnly A-A and B-B bondsState 1‘A’ Atoms‘B’ AtomsA-A, B-B, and A-B bondsState 2Image by MIT OpenCourseWare.22.14 – Intro to Nuclear MaterialsSlide 26
Obtaining ΔHmixState 1‘A’ AtomsState 2‘B’ Atomsz is thecoordinationnumber(here, z 4)Under whichconditionswill Hmix 0? 0? 0?Image by MIT OpenCourseWare.22.14 – Intro to Nuclear MaterialsSlide 27
Obtaining ΔHmixBond numbers before mixing:#𝐴𝐴 𝐴𝐴𝑧𝑧𝑁𝑁𝑎𝑎𝑎𝑎 𝑋𝑋𝐴𝐴 2#𝐵𝐵 𝐵𝐵Bond numbers after mixing:#𝐴𝐴 𝐴𝐴𝑧𝑧𝑁𝑁𝑎𝑎𝑎𝑎 𝑋𝑋𝐴𝐴 22#𝐵𝐵 𝐵𝐵𝑧𝑧𝑁𝑁𝑎𝑎𝑎𝑎 𝑋𝑋𝐵𝐵 22𝑧𝑧𝑁𝑁𝑎𝑎𝑎𝑎 𝑋𝑋𝐵𝐵 2#𝐴𝐴 𝐵𝐵 𝑧𝑧𝑁𝑁𝑎𝑎𝑎𝑎 𝑋𝑋𝐴𝐴 𝑋𝑋𝐵𝐵z coordination number (# bonds / atom)22.14 – Intro to Nuclear MaterialsSlide 28
Obtaining ΔHmixNext steps:– Obtain energy before & after mixing– Subtract to get change in mixing enthalpy22.14 – Intro to Nuclear MaterialsSlide 29
Obtaining ΔSmixExamine available number of microstates.AorBUse the Boltzmann equation:22.14 – Intro to Nuclear MaterialsSlide 30
Obtaining ΔGmixΔ𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚 𝑧𝑧𝑁𝑁𝑎𝑎𝑎𝑎 𝑋𝑋𝐴𝐴 𝑋𝑋𝐵𝐵22.14 – Intro to Nuclear Materials𝐸𝐸𝐴𝐴 𝐴𝐴 𝐸𝐸𝐵𝐵 𝐵𝐵𝐸𝐸𝐴𝐴 𝐵𝐵 2Slide 31
Drawing Free Energy Diagramsof One PhaseWhat happens to the free energy when.ΔHmix 0ΔSmix 0ΔHmix 0ΔSmix 0ΔHmix 0ΔSmix 0ΔHmix 0ΔSmix 0ΔHmix 0ΔSmix 0ΔHmix 0ΔSmix 0ΔHmix 0ΔSmix 0ΔHmix 0ΔSmix 0ΔHmix 0ΔSmix 022.14 – Intro to Nuclear MaterialsSlide 32
Drawing Free Energy Diagramsof One PhaseWhat about.22.14 – Intro to Nuclear MaterialsSlide 33
Drawing Free Energy Diagramsof One PhaseStart with the free energy of the twoseparate components in one phase.Add in the free energy of mixing.Then superimpose all possible phases.22.14 – Intro to Nuclear MaterialsSlide 34
Drawing Free Energy DiagramsImage: Q. Jiang, Z. Wen. “Thermodynamics Of Materials.” Available through MITLibraries at 718-0/page/1.ΔGmixPlot GA and GB,show how Hmixand TΔSmixchange Gtot Springer. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 35
Drawing Free Energy Diagramsof Multiple PhasesExamples:– Solid/liquid solution– Miscibility gap– Eutectic (zero solubility)– Eutectic (some solubility)– Intermetallic (ordered) compound22.14 – Intro to Nuclear MaterialsSlide 36
Free Energy Diagrams to PhaseDiagramsImage: Q. Jiang, Z. Wen. “Thermodynamics Of Materials.” Available through MITLibraries at 718-0/page/1.T2T1T3T3T2T1 Springer. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 37
Two-Phase Region CriterionImage: Q. Jiang, Z. Wen. “Thermodynamics Of Materials.” Available through MITLibraries at 718-0/page/1.T2T2 𝑨𝑨 𝑩𝑩 Chemical potential change isthe same at mixture(s) Springer. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 38
How will the phases form?Nucleation &Growth The Department of Organic and Polymeric Materials, TokyoInstitute of Technology.All rights reserved. This content isexcluded from our Creative Commons license.For moreinformation, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSpinodalDecompositionThis image is in the public domain.Wikimedia CommonsSlide 39
How will the phases form?Nucleation &Growth22.14 – Intro to Nuclear MaterialsSpinodalDecompositionSlide 40
Phase Diagram: Spinodal RegionCourtesy of W. Craig Carter. Used with permission.http://pruffle.mit.edu/ ccarter/3.21/Lecture 27/22.14 – Intro to Nuclear MaterialsSlide 41
Spinodal Decomposition EnergyImage: Q. Jiang, Z. Wen. “Thermodynamics Of Materials.” Available through MITLibraries at 718-0/page/1. Springer. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.22.14 – Intro to Nuclear MaterialsSlide 42
In-Class Example: W-ZrDraw the Gibbsfree energydiagram at 1000CSource: ASM Handbook, Volume 3: Alloy Phase Diagrams. Reprinted withpermission of ASM International .22.14 – Intro to Nuclear MaterialsSlide 43
In-Class Example: W-ZrαWSource: ASM Handbook, Volume 3: Alloy Phase Diagrams. Reprinted withpermission of ASM International .22.14 – Intro to Nuclear MaterialsZrW2Slide 44
MIT OpenCourseWarehttp://ocw.mit.edu22.14 Materials in Nuclear EngineeringSpring 2015For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Source: ASM Handbook, Volume 3: Alloy Phase Diagrams. Reprinted with permission of ASM International . 22.14 –Intro to Nuclear Materials. Reading Phase Diagrams: The . Lever Rule. Slide 17.
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Introduction of Chemical Reaction Engineering Introduction about Chemical Engineering 0:31:15 0:31:09. Lecture 14 Lecture 15 Lecture 16 Lecture 17 Lecture 18 Lecture 19 Lecture 20 Lecture 21 Lecture 22 Lecture 23 Lecture 24 Lecture 25 Lecture 26 Lecture 27 Lecture 28 Lecture
a time period. There are seven behavioral diagrams: Use Case Diagrams, Activity Diagrams, State Machine Diagrams, Communication Diagrams, Sequence Diagrams, Timing Diagrams and Interaction Overview Diagrams. UML 2 has introduced Composite Structure, Object, Timing and Interaction Overview diagrams.
node diagrams (N diagrams), node-link diagrams (NL diagrams) and node-link-groups diagrams (NLG diagrams). Each of these diagrams extends the previous one by making more explicit a characteristic of the input data. In N diagrams, a set of objects is depicted as points in a two or three dimensional space; see Figure1a. Clusters are typically .
Binary phase diagrams are most commonly used in alloy designing. The Gibbs phase rule is reduced to F C - P 1. (1 is for T). Fe-Ni, Cu-Ni, Ag-Au, Al 2 O 3-Cr 2 O 3, Pb-Sn and Fe-Fe 3 C are the examples for a two-component system. Classification of binary phase diagrams These have been classified based on: 1.
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Lecture #1: Bits, Bytes, and Binary CS106E Spring 2018, Young The binary number system underlies all modern computers. In this lecture we'll take a look at the binary number system and some of the implications of using binary numbers. Having a solid grounding in binary will set us up to explore digital images and digital music in the next two .
Class Diagrams etc. (e.g. Component Diagrams) Dynamic / Behavioral Modeling: capturing execution of the system Use Case Diagrams Sequence Diagrams State Chart Diagrams etc. (e.g. Activity Diagrams) UML Diagrams Models: high-level class relations Components: Class (rectangle) - Upper section: name of the class
