The document discusses phase diagrams and microstructures in binary alloy systems. It uses the Cu-Ni and Pb-Sn systems as examples. Some key points:
1) A binary phase diagram shows the phases present (solid, liquid, etc.) as a function of temperature and composition for a two-component system. It can be used to determine phases, phase compositions, and amounts at a given temperature and composition.
2) The Cu-Ni system is a continuous solid solution with a single α phase at all compositions. The Pb-Sn system is eutectic, with α, β, and liquid phases separated by solubility limits.
3) Eutectic microstructures form a
In situ XAFS studies of carbon supported Pt and PtNi(1:1) catalysts for the o...qjia
it\'s a presentation for APS Meeting In Iowa. It mainly introduces our work of rationalizing the superior reactivity of certain commercial alloy nanocatalysts by probing their physical and chemical properties through x-ray experiments and theoretical model simulation.
Tem for incommensurately modulated materialsJoke Hadermann
This presentation is a teaching lecture given on the International School on Aperiodic Crystals and explains how to index electron diffraction patterns taken from incommensurately modulated materials, with exercises, and gives some examples of HAADF-STEM and HRTEM images on incommensurately modulated materials.
Epitaxial growth of graphene on 6H-silicon carbide substrate by simulated an...Yoon Leong
We grew graphene epitaxially on 6H-SiC(0001) substrate by the simulated annealing method. The mechanisms that govern the growth process were investigated by testing two empirical potentials, namely, the widely used Tersoff potential and its more refined version published years later by Erhart and Albe (TEA potential). We evaluated the reasonableness of our layers of graphene by calculating carbon-carbon (i) average bond-length, (ii) binding energy. The annealing temperature at which the graphene structure just coming into view at approximately 1200 K is unambiguously predicted by TEA potential and close to the experimentally observed pit formation at 1298 K.
My PhD Thesis as I presented in my Preliminary Exam. Manmohan Dash
My PhD Thesis as I presented in my Preliminary Exam.
Manmohan Dash, Virginia Tech
A detailed description of the content in these slides are given in the linked article below. This I have quite more prepared for the layman in mind. So even if you are not versed in the intricate technical depth of particle physics, you are welcome to barge and enjoy my personal experiences as a particle physicist, as I was a decade ago and also you might enjoy some of the lay man explanation of the particle physics phenomena explained here.
http://mdashf.org/2015/06/09/my-phd-thesis-preliminary-exam/
In situ XAFS studies of carbon supported Pt and PtNi(1:1) catalysts for the o...qjia
it\'s a presentation for APS Meeting In Iowa. It mainly introduces our work of rationalizing the superior reactivity of certain commercial alloy nanocatalysts by probing their physical and chemical properties through x-ray experiments and theoretical model simulation.
Tem for incommensurately modulated materialsJoke Hadermann
This presentation is a teaching lecture given on the International School on Aperiodic Crystals and explains how to index electron diffraction patterns taken from incommensurately modulated materials, with exercises, and gives some examples of HAADF-STEM and HRTEM images on incommensurately modulated materials.
Epitaxial growth of graphene on 6H-silicon carbide substrate by simulated an...Yoon Leong
We grew graphene epitaxially on 6H-SiC(0001) substrate by the simulated annealing method. The mechanisms that govern the growth process were investigated by testing two empirical potentials, namely, the widely used Tersoff potential and its more refined version published years later by Erhart and Albe (TEA potential). We evaluated the reasonableness of our layers of graphene by calculating carbon-carbon (i) average bond-length, (ii) binding energy. The annealing temperature at which the graphene structure just coming into view at approximately 1200 K is unambiguously predicted by TEA potential and close to the experimentally observed pit formation at 1298 K.
My PhD Thesis as I presented in my Preliminary Exam. Manmohan Dash
My PhD Thesis as I presented in my Preliminary Exam.
Manmohan Dash, Virginia Tech
A detailed description of the content in these slides are given in the linked article below. This I have quite more prepared for the layman in mind. So even if you are not versed in the intricate technical depth of particle physics, you are welcome to barge and enjoy my personal experiences as a particle physicist, as I was a decade ago and also you might enjoy some of the lay man explanation of the particle physics phenomena explained here.
http://mdashf.org/2015/06/09/my-phd-thesis-preliminary-exam/
أفضل 10 أسئلة وأجوبة حول قوقل أدسنس AdSense وكيف ستم الموافقة على حساب ادسنس وكيف كيف يمكنك ربح المال على ادسنس وكيف تضع اعلانات أدسنس وهل جوجل ادسنس شرعية حقا .
How can diversification be used as a strategic marketing communications tool? We look at why the diversification trend is gathering pace and three ways brands can use diversification to grow.
Compratus Catálogo de Neumáticos de Inviernocompratus
Neumáticos de invierno. Encuentra las marcas que mayor confianza reportan al conductor: Kleber, Michelin, Firestone, Bridgestone, Hankook, Good Year, Pirelli, Fortuna, Minerva, Roadstone
كيف تستفيد من كتابة المواضيع في أدلة المقالات وتكسب من خلالها المال أو اشهار موقعك والحصول على زوار مع قائمة لبعض الدلائل ذات الجودة العالية لنشر المقالات .
Postsecondary lesson for pre-u students or form 6th students on mole concept, stoichiometry, limiting reagent, spectrometry and percent yield and percent purity.
Master Thesis Total Oxidation Over Cu Based Catalystsalbotamor
The evolution in the oxidation state of Cu and Ce in a benchmark catalyst is studied
under different conditions: temperature programmed reduction with propane and hydrogen,
and isothermal reduction with propane and hydrogen.
Analytical methods used involve operando X-ray absorption spectroscopy (XAS) in
transmission mode at the Cu K edge and Ce LIII edge, as well as online mass spectrometry
(MS) at the outlet of the reactor.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
1. 1
Chapter 9 - 1
Ch 9: Phase Diagrams
• Read: Ch 9 – general reading sections 1-6, careful study
sections 7-12, and 18-20. Plus all example problems. .
State of the Art (SoA) Project due dates:
eMemo w/3 proposals-via email, Sun. 7/10 11:59 pm. 1 page =15%
Final Paper Report +email –. Prefer Cover, Neat, stapled
due-7/19 (report format and sample reports available =85%
Chapter 9 -
Ch9:Do we know these terms?
– Gibb’s Phase Rule
– γ-Austenite,
– Cementite
– Pearlite
– Isomorphous
– Lever Rule
– α-Ferrite
– Eutectic
– Eutectoid
– Liquidus, Solidus,
Solvus lines etc.
2
– Terminal solid
Solution
– Tie line
– Martensite
– Hypoeutectic
– Hypereutectic
– Proeutectoid
– Hypoeutectoid
– hypereutectoid,
etc.
Chapter 9 - 3
Phase Equilibria: Solubility Limit
Introduction
– Solutions – solid solutions (alloys), single phase
– Mixtures – more than one phase
• Solubility Limit:
Max concentration for
which only a single phase
solution occurs.
Question: What is the
solubility limit at 20°C?
Answer: 65 wt% sugar.
If Co < 65 wt% sugar: syrup
If Co > 65 wt% sugar: syrup + sugar.
65
Sucrose/Water Phase Diagram
Pure
Sugar
Temperature(°C)
0 20 40 60 80 100
Co =Composition (wt% sugar)
L
(liquid solution
i.e., syrup)
Solubility
Limit L
(liquid)
+
S
(solid
sugar)20
40
60
80
100
Pure
Water
2. 2
Chapter 9 - 4
• Components:
The elements or compounds which are present in the mixture
(e.g., Al and Cu) there are 2.
• Phases:
The physically and chemically distinct material regions
that result (e.g., α and β). So, there are how many phases?
Aluminum-Copper Alloy
( a type of Bronze)
Components and Phases
α (darker
phase)
β (lighter
phase)
Adapted from
chapter-opening
photograph, Chapter
9, Callister 3e.
Chapter 9 - 5
Phase Equilibria
Crystal
Structure
electroneg r (nm)
Ni FCC 1.9 0.1246
Cu FCC 1.8 0.1278
• Both have the same crystal structure (FCC) and have
similar electronegativities and atomic radii (W. Hume –
Rothery rules) suggesting high mutual solubility.
Simple solution system (e.g., Ni-Cu solution)
• Result Ni and Cu are totally miscible in ALL proportions.
= ISOMORPHOUS ALLOY
Chapter 9 - 6
Binary Phase Diagrams: e.g. Cu-Ni.
• Indicate phases as function of T, Co, and P.
• For this course:
-binary systems: just 2 components.
-independent variables: T and Co (P = 1 atm is almost always used).
• Phase
Diagram
for Cu-Ni
system
Adapted from Fig. 9.3(a), Callister 7e.
(Fig. 9.3(a) is adapted from Phase
Diagrams of Binary Nickel Alloys, P. Nash
(Ed.), ASM International, Materials Park,
OH (1991).
• 2 phases:
L (liquid)
α (FCC solid solution)
• 3 phase fields:
L
L + α
α
wt% Ni20 40 60 80 1000
1000
1100
1200
1300
1400
1500
1600
T(°C)
L (liquid)
α
(FCC solid
solution)
3. 3
Chapter 9 - 7
wt% Ni20 40 60 80 1000
1000
1100
1200
1300
1400
1500
1600
T(°C)
L (liquid)
α
(FCC solid
solution)
Cu-Ni
phase
diagram
Phase Diagrams:EXPL
# and types of phases
• Rule 1: If we know T and Co, then we know:
--the # and types of phases present.
• Examples:
A(1100°C, 60):
1 phase: α
B(1250°C, 35):
2 phases: L + α
Adapted from Fig. 9.3(a), Callister 7e.
(Fig. 9.3(a) is adapted from Phase
Diagrams of Binary Nickel Alloys, P. Nash
(Ed.), ASM International, Materials Park,
OH, 1991).
B(1250°C,35)
A(1100°C,60)
Chapter 9 - 8
wt% Ni
20
1200
1300
T(°C)
L (liquid)
α
(solid)
30 40 50
Cu-Ni
system
Phase Diagrams:EXPL
composition of phases
• Rule 2: If we know T and Co, then we know:
--the composition of each phase.
• Examples:
TA
A
35
Co
32
CL
At TA = 1320°C:
Only Liquid (L)
CL = Co ( = 35 wt% Ni)
At TB = 1250°C:
Both α and L
CL = Cliquidus ( = 32 wt% Ni here)
Cα = Csolidus ( = 43 wt% Ni here)
At TD = 1190°C:
Only Solid ( α)
Cα = Co ( = 35 wt% Ni)
Co = 35 wt% Ni
Adapted from Fig. 9.3(b), Callister 7e.
(Fig. 9.3(b) is adapted from Phase Diagrams
of Binary Nickel Alloys, P. Nash (Ed.), ASM
International, Materials Park, OH, 1991.)
B
TB
D
TD
tie line
4
Cα
3
Chapter 9 - 9
• Tie line – connects the phases in equilibrium with
each other - essentially an isothermal line
The Lever Rule
How much of each phase?
Think of it as a lever (teeter-totter)
ML Mα
R S
RMSM L ⋅=⋅α
L
L
LL
L
L
CC
CC
SR
R
W
CC
CC
SR
S
MM
M
W
−
−
=
+
=
−
−
=
+
=
+
=
α
α
α
α
α
00
wt% Ni
20
1200
1300
T(°C)
L (liquid)
α
(solid)
30 40 50
B
TB
tie line
CoCL Cα
SR
Adapted from Fig. 9.3(b),
Callister 7e.
4. 4
Chapter 9 - 10
• Rule 3: If we know T and Co, then we know:
--the amount of each phase (given in wt%).
• Examples:
At TA: Only Liquid (L)
WL = 100 wt%, Wα = 0
At TD: Only Solid ( α)
WL = 0, Wα = 100 wt%
Co = 35 wt% Ni
Adapted from Fig. 9.3(b), Callister 7e.
(Fig. 9.3(b) is adapted from Phase Diagrams of
Binary Nickel Alloys, P. Nash (Ed.), ASM
International, Materials Park, OH, 1991.)
Phase Diagrams:
weight fractions of phases
wt% Ni
20
1200
1300
T(°C)
L (liquid)
α
(solid)
30 40 50
Cu-Ni
system
TA
A
35
Co
32
CL
B
TB
D
TD
tie line
4
Cα
3
R S
At TB: Both α and L
%73
3243
3543
wt=
−
−
=
= 27 wt%
WL
= S
R +S
Wα
= R
R +S
Chapter 9 - 11
wt% Ni
20
1200
1300
30 40 50
110 0
L (liquid)
α
(solid)
T(°C)
A
35
Co
L: 35wt%Ni
Cu-Ni
system
• Phase diagram:
Cu-Ni system.
• System is:
--binary
i.e., 2 components:
Cu and Ni.
--isomorphous
i.e., complete
solubility of one
component in
another; α phase
field extends from
0 to 100 wt% Ni.
Adapted from Fig. 9.4,
Callister 7e.
• Consider
Co = 35 wt%Ni.
Development of microstructure upon cooling
4635
43
32
α: 43 wt% Ni
L: 32 wt% Ni
L: 24 wt% Ni
α: 36 wt% Ni
Bα: 46 wt% Ni
L: 35 wt% Ni
C
D
E
24 36
Chapter 9 - 12
• Cα changes as we solidify.
• Cu-Ni case:
• Fast rate of cooling:
Cored structure
• Slow rate of cooling:
Equilibrium structure
First α to solidify has Cα = 46 wt% Ni.
Last α to solidify has Cα = 35 wt% Ni.
Cored vs Equilibrium Phases
First α to solidify:
46 wt% Ni
Uniform Cα:
35 wt% Ni
Last α to solidify:
< 35 wt% Ni
Provided the 35% soluton
is mantained..
How’s it possible
that average is
same as the
outer comp. Of
the cored grain?
5. 5
Chapter 9 - 13
Mechanical Properties: Cu-Ni System
• Effect of solid solution strengthening on:
--Tensile strength (TS) --Ductility (%EL,%AR)
--Peak as a function of Co --Min. as a function of Co
Adapted from Fig. 9.6(a), Callister 7e. Adapted from Fig. 9.6(b), Callister 7e.
TensileStrength(MPa)
Composition, wt% Ni
Cu Ni
0 20 40 60 80 100
200
300
400
TS for
pure Ni
TS for pure Cu
Elongation(%EL)
Composition, wt% Ni
Cu Ni
0 20 40 60 80 100
20
30
40
50
60
%EL for
pure Ni
%EL for pure Cu
Chapter 9 - 14
Review
Isomorphous Alloy
Lever Rule
Phase Analysis 3 main items
phases present
?
?
Solidus, Liquidus, Vapodus
Tie Line
Microstructure development
Cored structure ?
Chapter 9 - 15
: Min. melting TE
2 components
has a special composition
with a min. melting T.
Adapted from Fig. 9.7,
Callister 7e.
Binary-Eutectic Systems
• Eutectic transition
L(CE) α(CαE) + β(CβE)
• 3 single phase regions
(L, α, β ) total regions=?
• Limited solubility:
α: mostly Cu
β: mostly Ag
• TE : No liquid below TE
• @CE
composition
Ex.: Cu-Ag system
Cu-Ag
system
L (liquid)
α L + α
L+ββ
α + β
Co , wt% Ag
20 40 60 80 1000
200
1200
T(°C)
400
600
800
1000
CE
TE 8.0 71.9 91.2
779°C
6. 6
Chapter 9 - 16
L+α
L+β
α + β
200
T(°C)
18.3
C, wt% Sn
20 60 80 1000
300
100
L (liquid)
α 183°C
61.9 97.8
β
• For a 40 wt% Sn-60 wt% Pb alloy at 150°C, find...
--the phases present: Pb-Sn
system
EX: Pb-Sn Eutectic System (1)
α + β
--compositions of phases:
CO = 40 wt% Sn
--the relative amount
of each phase:
150
40
Co
11
Cα
99
Cβ
SR
Cα = 11 wt% Sn
Cβ = 99 wt% Sn
Wα=
Cβ - CO
Cβ - Cα
=
99 - 40
99 - 11
=
59
88
= 67 wt%
S
R+S
=
Wβ =
CO - Cα
Cβ - Cα
=
R
R+S
=
29
88
= 33 wt%=
40 - 11
99 - 11
Adapted from Fig. 9.8,
Callister 7e.
Chapter 9 - 17
L+β
α + β
200
T(°C)
C, wt% Sn
20 60 80 1000
300
100
L (liquid)
α β
L+α
183°C
• For a 40 wt% Sn-60 wt% Pb alloy at 220°C, find...
--the phases present: Pb-Sn
system
Adapted from Fig. 9.8,
Callister 7e.
EX: Pb-Sn Eutectic System (2)
α + L
--compositions of phases:
CO = 40 wt% Sn
--the relative amount
of each phase:
Wα =
CL - CO
CL - Cα
=
46 - 40
46 - 17
=
6
29
= 21 wt%
WL =
CO - Cα
CL - Cα
=
23
29
= 79 wt%
40
Co
46
CL
17
Cα
220
SR
Cα = 17 wt% Sn
CL = 46 wt% Sn
Chapter 9 - 18
• Co < 2 wt% Sn
• Result:
--at extreme ends
--polycrystal of α grains
i.e., only one solid phase.
Adapted from Fig. 9.11,
Callister 7e.
Microstructures
in Eutectic Systems: I
0
L+ α
200
T(°C)
Co, wt% Sn
10
2
20
Co
300
100
L
α
30
α+β
400
(room T solubility limit)
TE
(Pb-Sn
System)
α
L
L: Co wt% Sn
α: Co wt% Sn
7. 7
Chapter 9 - 19
• 2 wt% Sn < Co < 18.3 wt% Sn
• Result:
Initially liquid + α
then α alone
finally two phases
α polycrystal
fine β-phase inclusions
Adapted from Fig. 9.12,
Callister 7e.
Microstructures
in Eutectic Systems: II
Pb-Sn
system
L + α
200
T(°C)
Co , wt% Sn
10
18.3
200
Co
300
100
L
α
30
α+ β
400
(sol. limit at TE)
TE
2
(sol. limit at Troom)
L
α
L: Co wt% Sn
α
β
α: Co wt% Sn
Chapter 9 - 20
• Co = CE
• Result: Eutectic microstructure (lamellar structure)
--alternating layers (lamellae) of α and β crystals.
Adapted from Fig. 9.13,
Callister 7e.
Microstructures
in Eutectic Systems: III
Adapted from Fig. 9.14, Callister 7e.
160µm
Micrograph of Pb-Sn
eutectic
microstructure
Pb-Sn
system
L+β
α + β
200
T(°C)
C, wt% Sn
20 60 80 1000
300
100
L
α β
L+α
183°C
40
TE
18.3
α: 18.3 wt%Sn
97.8
β: 97.8 wt% Sn
CE
61.9
L: Co wt% Sn
Chapter 9 - 21
• 18.3 wt% Sn < Co < 61.9 wt% Sn e.g. 40% Sn
• Result: α crystals and a eutectic microstructure
Microstructures
in Eutectic Systems: IV
18.3 61.9
SR
97.8
SR
primary α
eutectic α
eutectic β
WL = (1-Wα) = 50 wt%
Cα = 18.3 wt% Sn
CL = 61.9 wt% Sn
S
R + S
Wα= = 50 wt%
• Just above TE :
• Just below TE :
Cα = 18.3 wt% Sn
Cβ = 97.8 wt% Sn
S
R + S
Wα= = 73 wt%
Wβ = 27 wt%
Adapted from Fig. 9.16,
Callister 7e.
Pb-Sn
system
L+β200
T(°C)
Co, wt% Sn
20 60 80 1000
300
100
L
α β
L+α
40
α+β
TE
L: Co wt% Sn Lα
L
α
8. 8
Chapter 9 - 22
L+α
L+β
α + β
200
Co, wt% Sn20 60 80 1000
300
100
L
α β
TE
40
(Pb-Sn
System)
Hypoeutectic & Hypereutectic
Adapted from Fig. 9.8,
Callister 7e. (Fig. 9.8 adapted from
Binary Phase Diagrams, 2nd ed.,
Vol. 3, T.B. Massalski (Editor-in-
Chief), ASM International, Materials
Park, OH, 1990.)
160 µm
eutectic micro-constituent
Adapted from Fig. 9.14,
Callister 7e.
hypereutectic: (illustration only)
β
β
β
β
β
β
Adapted from Fig. 9.17, Callister 7e.
(Illustration only)
(Figs. 9.14 and 9.17 from
Metals Handbook, 9th ed.,
Vol. 9, Metallography and
Microstructures, American
Society for Metals,
Materials Park, OH, 1985.)
175 µm
α
α
α
α
α
α
hypoeutectic: Co = 50 wt% Sn
Adapted from
Fig. 9.17, Callister 7e.
T(°C)
61.9
eutectic
eutectic: Co =61.9wt% Sn
Chapter 9 - 23
Review
Binary Eutectic System
Hypo and hyper eutectic alloys
Eutectic grain structure
Eutectic system phase analyses
Eutectic system microstructure formation
Cored structure of grains
Phase Analysis
phases present
?
?
Eutectoid (not Eutectic system)
Composition of phases
Wt% of phases
Chapter 9 - 24
Other Types:Eutectoid & Peritectic
Cu-Zn Phase diagram
Adapted from
Fig. 9.21, Callister 7e.
Eutectoid transition δ γ + ε
Peritectic transition γ + L δ
Identify
Eutectoid
Pt.
Now identify
a Peritectic
Pt.
Another ?
P
9. 9
Chapter 9 - 25
Source: www.substec.com
Chapter 9 - 26
Iron-Carbon (Fe-C) Phase Diagram
• 2 important
points
-Eutectoid (B):
γ ⇒ α +Fe3C
-Eutectic (A):
L ⇒ γ +Fe3C
Adapted from Fig. 9.24,Callister 7e.
Fe3C(cementite)
1600
1400
1200
1000
800
600
400
0 1 2 3 4 5 6 6.7
L
γ
(austenite)
γ+L
γ+Fe3C
α+Fe3C
L+Fe3C
δ
(Fe) Co, wt% C
1148°C
T(°C)
α 727°C = Teutectoid
A
SR
4.30
Result: Pearlite =
alternating layers of
α and Fe3C phases
120 µm
(Adapted from Fig. 9.27, Callister 7e.)
γ γ
γγ
R S
0.76
Ceutectoid
B
Fe3C (cementite-hard)
α (ferrite-soft)
Chapter 9 - 27
Hypoeutectoid Steel
Adapted from Figs. 9.24
and 9.29,Callister 7e.
(Fig. 9.24 adapted from
Binary Alloy Phase
Diagrams, 2nd ed., Vol.
1, T.B. Massalski (Ed.-in-
Chief), ASM International,
Materials Park, OH,
1990.)
Fe3C(cementite)
1600
1400
1200
1000
800
600
400
0 1 2 3 4 5 6 6.7
L
γ
(austenite)
γ+L
γ + Fe3C
α+ Fe3C
L+Fe3C
δ
(Fe) Co, wt% C
1148°C
T(°C)
α
727°C
(Fe-C
System)
C0
0.76
Adapted from Fig. 9.30,Callister 7e.
proeutectoid ferritepearlite
100 µm
Hypoeutectoid
steel
R S
α
wα =S/(R+S)
wFe3
C
=(1-wα)
wpearlite = wγ
pearlite
r s
wα =s/(r+s)
wγ =(1- wα)
γ
γ γ
γα
α
α
γγ
γ γ
γ γ
γγ
10. 10
Chapter 9 - 28
Hypereutectoid Steel
Fe3C(cementite)
1600
1400
1200
1000
800
600
400
0 1 2 3 4 5 6 6.7
L
γ
(austenite)
γ+L
γ +Fe3C
α +Fe3C
L+Fe3C
δ
(Fe) Co, wt%C
1148°C
T(°C)
α
Adapted from Figs. 9.24
and 9.32,Callister 7e.
(Fig. 9.24 adapted from
Binary Alloy Phase
Diagrams, 2nd ed., Vol.
1, T.B. Massalski (Ed.-in-
Chief), ASM International,
Materials Park, OH,
1990.)
(Fe-C
System)
0.76
Co
Adapted from Fig. 9.33,Callister 7e.
proeutectoid Fe3C
60 µmHypereutectoid
steel
pearlite
R S
wα =S/(R+S)
wFe3C =(1-wα)
wpearlite = wγ
pearlite
sr
wFe3C =r/(r+s)
wγ =(1-w Fe3C )
Fe3C
γγ
γ γ
γγ
γ γ
γγ
γ γ
Chapter 9 - 29
Example: Phase Equilibria
For a AISI1040 ( how much wt% Fe) steel at a temperature just
below the eutectoid temperature(727°C), determine the
following:
a) What are the phases?
b) composition of phases Fe3C and ferrite (α)
c) the amount of carbide (cementite) in grams that forms per 100
g of steel
d) the amount of pearlite and proeutectoid ferrite (α)
Solutions next page
Use a ruler on the handout diagram and
show all lines and %C.
Chapter 9 - 30
Chapter 9 – Phase Equilibria
Solution:
g3.94
g5.7CFe
g7.5100
022.07.6
022.04.0
100x
CFe
CFe
3
CFe3
3
3
=α
=
=
−
−
=
−
−
=
α+ α
α
x
CC
CCo
b) the amount of carbide
(cementite) in grams that
forms per 100 g of steel
a) composition of Fe3C and ferrite (α)
CO = 0.40 wt% C
Cα = 0.022 wt% C
CFe C = 6.70 wt% C
3
Fe3C(cementite)
1600
1400
1200
1000
800
600
400
0 1 2 3 4 5 6 6.7
L
γ
(austenite)
γ+L
γ + Fe3C
α+ Fe3C
L+Fe3C
δ
Co, wt% C
1148°C
T(°C)
727°C
CO
R S
CFe C3Cα
11. 11
Chapter 9 - 31
Chapter 9 – Phase Equilibria
c. the amount of pearlite and proeutectoid ferrite (α)
note: amount of pearlite = amount of γ just above TE
Co = 0.40 wt% C
Cα = 0.022 wt% C
Cpearlite = Cγ = 0.76 wt% C
γ
γ + α
=
Co −Cα
Cγ −Cα
x 100 = 51.2 g
pearlite = 51.2 g
proeutectoid α = 48.8 g
Fe3C(cementite)
1600
1400
1200
1000
800
600
400
0 1 2 3 4 5 6 6.7
L
γ
(austenite)
γ+L
γ + Fe3C
α+ Fe3C
L+Fe3C
δ
Co, wt% C
1148°C
T(°C)
727°C
CO
R S
CγCα
Chapter 9 - 32
Alloying Steel with More Elements
• Teutectoid changes: • Ceutectoid changes:
Adapted from Fig. 9.34,Callister 7e. (Fig. 9.34
from Edgar C. Bain, Functions of the Alloying
Elements in Steel, American Society for Metals,
1939, p. 127.)
Adapted from Fig. 9.35,Callister 7e. (Fig. 9.35
from Edgar C. Bain, Functions of the Alloying
Elements in Steel, American Society for Metals,
1939, p. 127.)
TEutectoid(°C)
wt. % of alloying elements
Ti
Ni
Mo
Si
W
Cr
Mn
wt. % of alloying elements
Ceutectoid(wt%C)
Ni
Ti
Cr
Si
Mn
W
Mo
Chapter 9 - 33
Practice Problem 9.66
• Teutectoid changes:
TEutectoid(°C)
wt. % of alloying elements
Ti
Ni
Mo
Si
W
Cr
Mn
6% Mn
So:
TE=700F
Contd.
Alloy Steel has 6% Mn,
and .25% C
TE=?,
%Eutectoid C=?
ProEutectoid Phase = ?
12. 12
Chapter 9 - 34
Eutectoid %C
• Ceutectoid changes:
wt. % of alloying elements
Ceutectoid(wt%C)
Ni
Ti
Cr
Si
Mn
W
Mo
From figure Eutectoid
Mixture happens at 0.44% C
If mixture has .25% C –
Then it is left of eutectoid
point, i.e. proeutectoid
phase is Ferrite
If %C in mixture is >
Eutectoid Mixture then
proeutectoid phase would
have been Cementite
Chapter 9 - 35
• Phase diagrams are useful tools to determine:
--the number and types of phases in an alloy,
--the wt% of each phase,
--and the composition of each phase
for a given T and composition of the system.
• Alloying to produce a solid solution usually
--increases the tensile strength (TS)
--decreases the ductility.
• Binary eutectics and binary eutectoids allow for
a range of microstructures.
Summary