K S T S ' = K L T L ' + vl v

Size: px
Start display at page:

Download "K S T S ' = K L T L ' + vl v"

Transcription

1 Heat Flow and Interface Stability Elemental metals - solidification rate controlled by rate at which latent of fusion can be conducted away from the solid/liquid interface Heat conduction can be either into the solid OR liquid depending on temperature gradient near the interface Case I: Solid growing into superheated liquid Solid/liquid interface growing with a velocity v Temperature gradients in both solid and liquid with interface at melting temp. T m Planar solid/liquid interface moving with velocity v, heat flow balance K S T S ' = K L T L ' + vl v K s are the thermal conductivities T s are the thermal gradients L V is the latent heat of fusion The above equation holds for growth of any planar interface even when heat is conducted into the liquid (T L < 0) Consider a small solid protrusion at the solid/liquid interface growing into the liquid Locally at the protrusion - temp. gradient into the liquid is increased, temp. gradient in solid decreases More heat flow from the liquid into the protrusion, slower rate of heat Phase extraction Transformations into the solid 1

2 Therefore, slower rate of growth of the solid at the protrusion as compared with the planar regions - solid protrusion is removed with time Interface protrusion is unstable Case II: Solid growing into undercooled or supercooled liquid Prostrusion at solid/liquid interface - negative temperature gradient at the interface becomes more negative - steeper gradient in liquid Faster rate of heat extraction into the liquid near the protrusion Solid protrusion grows faster Protrusions at interface are stable Planar solid/liquid interface growing into a supercooled liquid is inherently unstable Case I type situation (heat conduction through the solid) typically takes place when the solidification takes place from the mould walls - cooler than the molten liquid 2

3 Case II type situation (heat conduction into the liquid during solidification) - takes place during the initial stages of solidification for nucleation taking place on heterogeneous nucleation sites within the melt (e.g. impurity particles) - substantial undercooling (or supercooling) of the liquid might be required Solid nucleus forming on an impurity particle will be growing into a undercooled liquid - latent heat conducted into the liquid Solid particle will develop many stable protrusions in different directions during growth - arms will grow from the solid particle Initially spherical nucleus Interface becomes unstable Starts developing primary arms in many directions - usually crystallographic (e.g. for cubic metals along <001> directions along the cube axes) As primary arms grow and elongate, the interfaces become unstable and break up forming secondary arms, then tertiary arms and so on Shape of this type of solid - Dendrite (comes from the Greek word for tree) Dendritic growth morphology In pure metals these dentrites are referred to as thermal dendrites 3

4 Solidification of Single Phase Alloys Consider a binary alloy with the phase diagram as shown below: Liquidus and solidus are considered straight lines Define partition function as: k = X S X L X S and X L are the equilibrium solute contents at the ends of the tie line at a certain temperature k - independent of temp. Solidification of such an alloy is a rather complex process - depends on a combination of temp. gradients, cooling rates, growth velocities Simplified case: Planar growth of liquid/solid interface Unidirectional heat flow or heat extractions along a single direction Special furnace in which heat flow occurs only along a single direction 4

5 Three limiting cases of solidification: 1. Infinitely slow (equilibrium) solidification. 2. Solidification with no diffusion in the solid but perfect mixing in the liquid. 3. Solidification with no diffusion in the solid and only diffusional mixing in the liquid Equilibrium solidification: easiest case Alloy of composition X 0 starts solidifying at temperature T 1. First solid to form has composition, kx 0. Cooling further below T 1, more solid is formed. Cooling rate is sufficiently slow for diffusion to take place in the solid phase allowing for equilibrium homogeneous solid composition to be achieved Relative amounts of solid and liquid at any temp. - lever rule Since solidification is 1D, solute conservation implies that the shaded areas in the adjacent figure are equal Solidification is completed at T 3 and the last solidifying liquid has composition X 0 /k 5

6 No Diffusion in Solid, Perfect Mixing in Liquid: Often cooling rate is too rapid for substantial diffusion in the growing solid phase - assume no diffusion in the solid phase Liquid composition is kept homogeneous during cooling by continuous stirring 1D heat extraction as previous case: Solidification starts at temp. T 1 First solid to form has composition kx 0 < X 0, purer than the liquid from which it forms Solute rejected into the liquid - raises its composition above X 0 Temp. of interface has to be reduced before further solidification occurs - next layer of solid to form has a composition slightly richer in solute than kx 0. As process continues, liquid gets progressively richer in solute and solidification takes place at progressively lower temperatures At any temperature local equilibrium is maintained at the interface - solid and liquid compositions given by end points of tie line But since no diffusion in the solid is permitted the layers of solid forming retain their original compositions Therefore, mean composition of the solid is always lower than the interface solid composition (given by the phase diagram) - shown by the dashed line below: 6

7 Relative amounts of solid and liquid given by level rule applied to X S and X L. Liquid composition can become much richer than X 0 /k during solidification and even reach the eutectic composition X E. Soldification can finish by the final liquid undergoing eutectic solidification and forming a two phase (α + β) structure Average composition after complete solidification is still X 0 but the profile looks very different as compared to equilibrium solidification 7

8 Variation of X S along solidified bar obtained by equating solute rejected by small (infinitesimal) layer of solid formed to solute increase in the liquid ( X L X S )df S = ( 1 f S )dx L X S = kx 0 1 f ( ( S ) k 1 ) X L = X 0 f ( k 1) L f S is the volume fraction of solid Integrating using the boundary condition X S = kx 0 when f S = 0 Above equations are known as the non-equilibrium lever rule or Scheil equations 8

9 Cellular and Dendritic Solidification Diffusion of solute away from growing solid into liquid during alloy solidification - analogous to conduction of latent heat of fusion into liquid during pure metal solidification Complication - solute gradient ahead of solid/liquid interface - variation in equilibrium solidification temperature (liquidus line) Actual liquid temperature gradient can follow any line, e.g., T L At steady-state, at the interface, T L = T e = T 3 Temp. gradient T L lies below the critical T e value - so liquid is supercooled below its equilibrium solidification temp. - constitutional supercooling (arising from compositional or constitutional effects) 9

10 Stable protrusions can form on a planar interface during alloy soldification provided a region of constitutional supercooling exists ahead of the growing solid For the T L shown, the temp. of the tip of the protrusion will be higher than that of the surrounding interface - unlike pure metal solidification all the interface need not be isothermal in alloy solidification As long as tip temp. is < local liquidus temp., protrusion can still grow If temp. in liquid (T L ) > critical temp. gradient (T e ), then the tip temp. will exceed the local liquidus temp. and the protrusion will melt back Under steady-state growth, the critical temp. gradient can be calculated as follows: T L ' ( ) ( ) > T 1 T 3 D / v Where T 1 and T 3 are the liquidus and solidus temps. for comp. X 0 Regrouping, condition for no constitutional supercooling is, T L ' ( ) v > T 1 T 3 D T 1 -T 3 is the equilibrium freezing range of the alloy Planar front solidification is most difficult in case of alloys with a large equilibrium freezing range and high rates of solidification Usually, alloys never solidify with a planar solidification front - only under very specially controlled conditions Temp. gradients and growth rates are not individually controllable but depend in a complex manner on the rate at which heat is conducted away from solidifying alloy 10

11 Process of breakdown of an initially planar solidification front can be shown as below: Formation of first protrusion - lateral rejection of solute - solute pileup at the base of protrusion - lowers equilibrium solidification temp. locally - causes formation of recesses - triggers the formation of other protrusions Protrusions develop into long arms, or cells, parallel to the direction of heat flow - cellular solidification Lateral solute rejection concentrates at the cell walls - last liquid to solidify at lowest temperature Tips of the cells grow into the hottest liquid - therefore have minimum solute concentration Liquid between the cells - enriched in solute may even reach the eutectic composition and then the cell walls may have a second phase Cells have the same orientation as their neighbors and can join together to form single grain 11

12 Cellular solidification is stable only for certain range of temp. gradients - if gradient is too small, the cells or primary arms start developing secondary arms, tertiary arms.etc. - dendritic solidification Reason from cells to dendrites is not fully understood Probably associated with the creation of constitutional supercooling within the liquid entrapped between the walls of growing cells - causes interface instabilities in the lateral direction (perpendicular to the growth direction of primary cellular arms) For unidirectional solidification to continue, there should be minimal temp. gradient that develops in the lateral direction - perpendicular to growth direction Therefore, typically the cell arm spacing is such that this lateral gradient is reduced as much as possible - experimentally it is observed that with faster cooling rates the spacing decreases - consistent since faster cooling rates would allow less time for solute diffusion into the liquid between the cellular arms - reducing the spacing reduces the probability of developing constitutional supercooling 12

Phase Transformation in Materials

Phase Transformation in Materials 2015 Fall Phase Transformation in Materials 11. 11. 2015 Eun Soo Park Office: 33-313 Telephone: 880-7221 Email: espark@snu.ac.kr Office hours: by an appointment 1 Contents for previous class Solidification:

More information

Module 22. Solidification & Binary Phase Diagrams V. Lecture 22. Solidification & Binary Phase Diagrams V

Module 22. Solidification & Binary Phase Diagrams V. Lecture 22. Solidification & Binary Phase Diagrams V Module 22 Solidification & Binary Phase Diagrams V ecture 22 Solidification & Binary Phase Diagrams V 1 NPTE Phase II : IIT Kharagpur : Prof. R. N. Ghosh, Dept of Metallurgical and Materials Engineering

More information

Lecture 31: Principles of Solidification of Steel. Key words: Solidification, planar growth, dendritic growth, casting, constitutional supercooling

Lecture 31: Principles of Solidification of Steel. Key words: Solidification, planar growth, dendritic growth, casting, constitutional supercooling Lecture 31: Principles of Solidification of Steel Contents: Preamble Solidification variables Equilibrium solidification Non equilibrium solidification Microstructure development Key words: Solidification,

More information

Lecture 6: Solidification of Single Phase Alloys

Lecture 6: Solidification of Single Phase Alloys Lecture 6: Solidification of Single Phase Alloys 1 Zone Melting Process of zone melting: Start with a solid alloy bar with uniform cross-section. Place the bar horizontally. Only melt the bar within a

More information

SOLIDIFICATION, PHASE DIAGRAM & STEELS

SOLIDIFICATION, PHASE DIAGRAM & STEELS MODULE TWO SOLIDIFICATION, PHASE DIAGRAM & STEELS 4. SOLIDIFICATION Introduction Mechanism of solidification - crystallization and development of cast structure - nucleation and grain growth - dendritic

More information

Metallurgy - Lecture (2) Solidification

Metallurgy - Lecture (2) Solidification Metallurgy - Lecture (2) Solidification When molten metal enters a mold cavity, its heat is transferred through the mold wall. In the case of pure metals and eutectics, the solidification proceeds layer-bylayer

More information

EMA5001 Lecture 15 Other Issues with Metal Solidification by Zhe Cheng

EMA5001 Lecture 15 Other Issues with Metal Solidification by Zhe Cheng EMA5001 Lecture 15 Other Issues with Metal Solidification 016 by Zhe Cheng Eutectic Solidification L α + β 67 wt.% Al-wt% Cu eutectic Classification Normal Lamellar or other structures Both solid phase

More information

Learning Objectives. Chapter Outline. Solidification of Metals. Solidification of Metals

Learning Objectives. Chapter Outline. Solidification of Metals. Solidification of Metals Learning Objectives Study the principles of solidification as they apply to pure metals. Examine the mechanisms by which solidification occurs. - Chapter Outline Importance of Solidification Nucleation

More information

Two Metals Completely Soluble in the Liquid State and Completely Insoluble in the solid state

Two Metals Completely Soluble in the Liquid State and Completely Insoluble in the solid state Two Metals Completely Soluble in the Liquid State and Completely Insoluble in the solid state Technically, no two metals are completely insoluble in each other. However, in some cases the solubility is

More information

Pre-Course Reading for ESI s Solidification Course

Pre-Course Reading for ESI s Solidification Course Pre-Course Reading for ESI s Solidification Course A. B. Phillion, J. Dantzig The primary goal of ESI s Solidification Course is to relate material properties and solidification processing conditions to

More information

Thermal supercooling induced dendritic solidification

Thermal supercooling induced dendritic solidification Thermal supercooling induced dendritic solidification To show the formation of dendrites during the solidification of a supercooled melt (of a pure material) Course Name: Phase transformations and heat

More information

Chapter 10, Phase Transformations

Chapter 10, Phase Transformations Chapter Outline: Phase Transformations Heat Treatment (time and temperature) Microstructure Kinetics of phase transformations Homogeneous and heterogeneous nucleation Growth, rate of the phase transformation

More information

Numerical Simulation of Dendrite Growth during Solidification

Numerical Simulation of Dendrite Growth during Solidification Freund Publishing House Ltd. International Journal of Nonlinear Sciences and Numerical Simulation, 7(2), 171-176, 2006 Numerical Simulation of Dendrite Growth during Solidification X. Yao a b, B. He b,

More information

EMA5001 Lecture 13 Solidification via Heterogeneous Nucleation, Growth of Pure Solid from Liquid by Zhe Cheng

EMA5001 Lecture 13 Solidification via Heterogeneous Nucleation, Growth of Pure Solid from Liquid by Zhe Cheng EMA5001 Lecture 1 ification ia Heterogeneous Nucleation, Growth of Pure from 016 by Zhe Cheng EMA 5001 Physical Properties of Materials Zhe Cheng (016) 1 Heterogeneous Nucleation Heterogeneous Nucleation

More information

RUNNING HOT. Sub-topics. Fuel cells Casting Solidification

RUNNING HOT. Sub-topics. Fuel cells Casting Solidification RUNNING HOT Sub-topics 1 Fuel cells Casting Solidification CONCEPT OF FUEL CELLS International concerns regarding the emission of greenhouse gases and the trend toward distributed power generation are

More information

Solidification. Nov. 2010

Solidification. Nov. 2010 Solidification Nov. 2010 Rapid Solidification (10 5 K/s) Rapidly cool or quench to produce amorphous or glassy structure (metallic glass) Rapid Solidification Cooling

More information

ENGR 151: Materials of Engineering LECTURE #14: PHASE DIAGRAMS

ENGR 151: Materials of Engineering LECTURE #14: PHASE DIAGRAMS ENGR 151: Materials of Engineering LECTURE #14: PHASE DIAGRAMS ANNOUNCEMENTS Midterm #2 Monday, May 1. Review on Wednesday, April 26. Chapters 4, 6, 7, 8 TERMINOLOGY Phase: Homogeneous portion of a system

More information

Solidification & Binary Phase Diagrams II. Solidification & Binary Phase Diagrams II

Solidification & Binary Phase Diagrams II. Solidification & Binary Phase Diagrams II Module 19 Solidification & inary Phase Diagrams II ecture 19 Solidification & inary Phase Diagrams II 1 NPTE Phase II : IIT Kharagpur : Prof. R. N. hosh, Dept of Metallurgical and Materials Engineering

More information

12/3/ :12 PM. Chapter 9. Phase Diagrams. Dr. Mohammad Abuhaiba, PE

12/3/ :12 PM. Chapter 9. Phase Diagrams. Dr. Mohammad Abuhaiba, PE Chapter 9 Phase Diagrams 1 2 Learning Objectives 1. Isomorphous and eutectic phase diagrams: a. label various phase regions b. Label liquidus, solidus, and solvus lines 2. Given a binary phase diagram

More information

ENGR 151: Materials of Engineering LECTURE #15: PHASE DIAGRAMS

ENGR 151: Materials of Engineering LECTURE #15: PHASE DIAGRAMS ENGR 151: Materials of Engineering LECTURE #15: PHASE DIAGRAMS TENSILE TESTING VIDEO https://www.youtube.com/watch?v=-qukvzo2jse PROPERTIES OF ISOMORPHOUS ALLOYS Solid solution strengthening For Ni-Cu

More information

Metal Casting. Manufacturing Processes for Engineering Materials, 5th ed. Kalpakjian Schmid 2008, Pearson Education ISBN No.

Metal Casting. Manufacturing Processes for Engineering Materials, 5th ed. Kalpakjian Schmid 2008, Pearson Education ISBN No. Metal Casting Important factors in casting Solidification of the metal from its molten state and accompanying shrinkage Flow of the molten metal into the mold cavity Heat transfer during solidification

More information

Solidification microstructure development

Solidification microstructure development Sadhana, Vol. 6, Parts 1 &, February April 001, pp. 5 34. Printed in India Solidification microstructure development G PHANIKUMAR and K CHATTOPADHYAY Department of Metallurgy, Indian Institute of Science,

More information

Analysis of Grain Selection during Directional Solidification of Gas Turbine Blades

Analysis of Grain Selection during Directional Solidification of Gas Turbine Blades Analysis of Grain Selection during Directional Solidification of Gas urbine Blades H. B. Dong Abstract In this paper the evolution of grain structure and the control of crystal orientation in gas turbine

More information

ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING MATERIALS C102 TUTORIAL 3 THERMAL EQUILIBRIUM (PHASE) DIAGRAMS

ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING MATERIALS C102 TUTORIAL 3 THERMAL EQUILIBRIUM (PHASE) DIAGRAMS ENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING MATERIALS C102 TUTORIAL 3 THERMAL EQUILIBRIUM (PHASE) DIAGRAMS UNIT OUTCOMES On successful completion of the unit the candidate will be able to: 1. Recognise

More information

Chapter 9: Phase Diagrams

Chapter 9: Phase Diagrams Chapter 9: Phase Diagrams IUE TO ADDE... Common types of phase diagrams Isomorphous Eutectic Others Phase diagram and microstructure evolution Chapter 9-1 What is a phase? What is a component? Class Exercise

More information

CHAPTER 9 PHASE DIAGRAMS

CHAPTER 9 PHASE DIAGRAMS CHAPTER 9 PHASE DIAGRAMS PROBLEM SOLUTIONS 9.14 Determine the relative amounts (in terms of mass fractions) of the phases for the alloys and temperatures given in Problem 9.8. 9.8. This problem asks that

More information

Materials and Minerals Science Course C: Microstructure. Eutectic Systems. A single-component melt solidifies directly to a single-component solid:

Materials and Minerals Science Course C: Microstructure. Eutectic Systems. A single-component melt solidifies directly to a single-component solid: Eutectic Systems 1.1 Eutectic Reactions A single-component melt solidifies directly to a single-component solid: Pure Liquid Pure Solid In the last practical we saw that a liquid solution solidifies into

More information

Diffusional Transformations in Solids

Diffusional Transformations in Solids Diffusional Transformations in Solids The majority of phase transformations that occur in the solid state take place by thermally activated atomic movements. The transformations that will be dealt with

More information

Phase Diagrams of Pure Substances Predicts the stable phase as a function of P total and T. Example: water can exist in solid, liquid and vapor

Phase Diagrams of Pure Substances Predicts the stable phase as a function of P total and T. Example: water can exist in solid, liquid and vapor PHASE DIAGRAMS Phase a chemically and structurally homogenous region of a material. Region of uniform physical and chemical characteristics. Phase boundaries separate two distinct phases. A single phase

More information

TALAT Lecture Phase Diagrams. 14 pages, 13 Figures. Basic Level

TALAT Lecture Phase Diagrams. 14 pages, 13 Figures. Basic Level TALAT Lecture 1203 Phase Diagrams 14 pages, 13 Figures Basic Level prepared by M H Jacobs * Interdisciplinary Research Centre in Materials The University of Birmingham, UK (Based on approach adopted by

More information

MICROSTRUCTURE OF RAPIDLY SOLIDIFIED POWDERS

MICROSTRUCTURE OF RAPIDLY SOLIDIFIED POWDERS MICROSTRUCTURE OF RAPIDLY SOLIDIFIED POWDERS R. D. Field, A. R. Cox,J"' and H. L. Fraser?+ Department of Metallurgical and Mining Engineering University of Illinois Urbana, Illinois 61801 Individual rapidly

More information

Modeling: (i) thermal spray rapid solidification (ii) partially molten particle impact

Modeling: (i) thermal spray rapid solidification (ii) partially molten particle impact Modeling: (i) thermal spray rapid solidification (ii) partially molten particle impact Markus Bussmann Mechanical & Industrial Engineering Centre for Advanced Coating Technologies (CACT) University of

More information

Chapter 9 Phase Diagrams. Dr. Feras Fraige

Chapter 9 Phase Diagrams. Dr. Feras Fraige Chapter 9 Phase Diagrams Dr. Feras Fraige Chapter Outline Definitions and basic concepts Phases and microstructure Binary isomorphous systems (complete solid solubility) Binary eutectic systems (limited

More information

W. J. Boettinger, et al AO 3751

W. J. Boettinger, et al AO 3751 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (Wha, Dees R.,enwd) REPORT DOCUMENTATION PAGE B F~REDRUC t-in OR BEFREDCKuCLMnORK I. REPORT NUMBER 2. GOVT ACCESSION NO 3. RECIPIENT*S CATALOG NUMBER 14.

More information

Grain Refinement for Improved Lead-Free Solder Joint Reliability

Grain Refinement for Improved Lead-Free Solder Joint Reliability Grain Refinement for Improved Lead-Free Solder Joint Reliability K. Sweatman 1, S. D. McDonald 2, M. Whitewick 2, T. Nishimura 1, and K. Nogita 2 1. Nihon Superior Co., Ltd, Osaka, Japan 2. University

More information

Two Components System

Two Components System Two Components System Three independent variables: T, P, compositions In general, constant pressure (fixed parameter). P+F=C+1 Simple Eutectic System The binary eutectic phase diagram explains the chemical

More information

Phase Selection during Directional Solidification of Peritectic Alloys

Phase Selection during Directional Solidification of Peritectic Alloys Ames Laboratory Publications Ames Laboratory 5-2005 Phase Selection during Directional Solidification of Peritectic Alloys Thomas A. Lograsso Iowa State University, lograsso@ameslab.gov B. C. Fuh R. Trivedi

More information

Engineering Materials and Processes Lecture 9 Equilibrium diagrams

Engineering Materials and Processes Lecture 9 Equilibrium diagrams Lecture 9 Equilibrium diagrams Equilibrium diagrams Reference Text Higgins RA & Bolton, 2010. Materials for Engineers and Technicians, 5th ed, Butterworth Heinemann Section Ch 9 Additional Readings Callister,

More information

Binary Phase Diagrams - II

Binary Phase Diagrams - II Binary Phase Diagrams - II Note the alternating one phase / two phase pattern at any given temperature Binary Phase Diagrams - Cu-Al Can you spot the eutectoids? The peritectic points? How many eutectic

More information

MICROSTUCTURE OF CAST TITANIUM ALLOYS

MICROSTUCTURE OF CAST TITANIUM ALLOYS MATERIALS FORUM VOLUME 31-2007 Edited by J.M. Cairney and S.P. Ringer Institute of Materials Engineering Australasia MICROSTUCTURE OF CAST TITANIUM ALLOYS M.J. Bermingham, S.D. McDonald, M.S. Dargusch,

More information

Chapter 10: Phase Transformations

Chapter 10: Phase Transformations Chapter 10: Phase Transformations ISSUES TO ADDRESS... Transforming one phase into another takes time. Fe C FCC (Austenite) Eutectoid transformation Fe 3 C (cementite) + (ferrite) (BCC) How does the rate

More information

MACRO- AND MICROSTRUCTURES

MACRO- AND MICROSTRUCTURES CHAPTER 11 MACRO- AND MICROSTRUCTURES Movies from simulations relating to macro-micro models of solidification can be found at: http://solidification.org/movies/macro-micro. html 11.1 INTRODUCTION The

More information

MAE 212: Spring 2001 Lecture 14 PHASE DIAGRAMS AND EQUILIBRIUM MICROSTRUCTURES N. Zabaras

MAE 212: Spring 2001 Lecture 14 PHASE DIAGRAMS AND EQUILIBRIUM MICROSTRUCTURES N. Zabaras ME 212: Spring 2001 Lecture 14 PHSE DIGRMS ND EQUILIRIUM MICROSTRUCTURES N. Zabaras For more details on the topic read Chapter 9 of the Materials Science for Engineers by J. Shackelford, pp. 304 353. lso

More information

Chapter 10: Phase Transformations

Chapter 10: Phase Transformations Chapter 10: Phase Transformations ISSUES TO ADDRESS... Transforming one phase into another takes time. Fe (Austenite) Eutectoid transformation Fe 3 C (cementite) + C FCC (ferrite) (BCC) How does the rate

More information

Experiment A: Solidification and Casting

Experiment A: Solidification and Casting Experiment A: Solidification and Casting Introduction: The purpose of this experiment is to introduce students to the concepts of solidification and to study the development of solidification microstructures.

More information

solvent: component of a solution present in the greatest amount in alloy.

solvent: component of a solution present in the greatest amount in alloy. Phase Equilibrium Diagrams:- Phase equilibrium diagram is a graphic relationship between temperature and weight ratios of elements and alloys contribute to the built of the diagram. Phase diagrams provide

More information

8. Principles of Solidification

8. Principles of Solidification CBE4010 Introduction to Materials Science for Chemical Engineers 8. Principles of Solidification The Driving Force a Phase Change We expect a material to solidify when the liquid cools to just below its

More information

Phase diagrams wt% of carbon in Fe microstructure of a lead tin alloy of eutectic composition

Phase diagrams wt% of carbon in Fe microstructure of a lead tin alloy of eutectic composition Phase diagrams 0.44 wt% of carbon in Fe microstructure of a lead tin alloy of eutectic composition Primer Materials For Science Teaching Spring 2018 28.6.2018 What is a phase? A phase may be defined as

More information

Science and Engineering of Casting Solidification Second Edition

Science and Engineering of Casting Solidification Second Edition Science and Engineering of Casting Solidification Second Edition Doru Michael Stefanescu Science and Engineering of Casting Solidification Second Edition Doru Michael Stefanescu Department of Materials

More information

Simulation of Solute Redistribution during Casting and Solutionizing of Multi-phase, Multi-component Aluminum Alloys

Simulation of Solute Redistribution during Casting and Solutionizing of Multi-phase, Multi-component Aluminum Alloys Simulation of Solute Redistribution during Casting and Solutionizing of Multi-phase, Multi-component Aluminum Alloys F. Yi,* H. D. Brody* and J. E. Morral** * University of Connecticut, Storrs, CT 6269-336

More information

Chapter 6. Solidification

Chapter 6. Solidification Chapter 6 Solidification Almost all processing of technologically important metals includes a step where liquid material is cooled to form a solid. It is very common, for example, for the components of

More information

but T m (Sn0.62Pb0.38) = 183 C, so this is a common soldering alloy.

but T m (Sn0.62Pb0.38) = 183 C, so this is a common soldering alloy. T m (Sn) = 232 C, T m (Pb) = 327 C but T m (Sn0.62Pb0.38) = 183 C, so this is a common soldering alloy. T m (Au) = 1064 C, T m (Si) = 2550 C but T m (Au0.97Si0.03) = 363 C, so thin layer of gold is used

More information

the Phase Diagrams Today s Topics

the Phase Diagrams Today s Topics MME 291: Lecture 04 Interpretation of the Phase Diagrams Prof. A.K.M.B. Rashid Department of MME BUET, Dhaka Today s Topics Interpretation of phase diagrams Development of microstructures during equilibrium

More information

Phase Transformation in Materials

Phase Transformation in Materials 2016 Fall Phase Transformation in Materials 09. 28. 2016 Eun Soo Park Office: 33-313 Telephone: 880-7221 Email: espark@snu.ac.kr Office hours: by an appointment 1 Equilibrium in Heterogeneous Systems In

More information

Phase field simulation of the columnar dendritic growth and microsegregation in a binary alloy

Phase field simulation of the columnar dendritic growth and microsegregation in a binary alloy Vol 17 No 9, September 28 c 28 Chin. Phys. Soc. 1674-156/28/17(9)/3516-7 Chinese Physics B and IOP Publishing Ltd Phase field simulation of the columnar dendritic growth and microsegregation in a binary

More information

27-301, Fall 02, Rollett. Total marks = 100 (20 per question). 1 st Homework, due Sept. 6th

27-301, Fall 02, Rollett. Total marks = 100 (20 per question). 1 st Homework, due Sept. 6th 27-301, Fall 02, Rollett Total marks = 100 (20 per question). 1 st Homework, due Sept. 6th Notes/Answers The thermal histories asked for in this homework are not always unique defined so the homeworks

More information

Introduction to Phase Diagrams. Version 2.1. Andrew Green, MATTER Trevor Myers, UMIST/University of Manchester

Introduction to Phase Diagrams. Version 2.1. Andrew Green, MATTER Trevor Myers, UMIST/University of Manchester Introduction to Phase Diagrams Version 2.1 Andrew Green, MATTER Trevor Myers, UMIST/University of Manchester Assumed Pre-knowledge This module has been designed as a basic introduction to many of the concepts

More information

Chapter 9 Heat treatment (This chapter covers selective sections in Callister Chap. 9, 10 &11)

Chapter 9 Heat treatment (This chapter covers selective sections in Callister Chap. 9, 10 &11) Chapter 9 Heat treatment (This chapter covers selective sections in Callister Chap. 9, 10 &11) Study theme outcomes: After studying this chapter, students should or should be able to: - know and understand

More information

Evolution of the Specific Solid-Liquid Interface Area in Directional Solidification

Evolution of the Specific Solid-Liquid Interface Area in Directional Solidification Evolution of the Specific Solid-Liquid Interface Area in Directional Solidification Beckermann C 1), Neumann-Heyme H 2), Eckert K 2) 1 Department of Mechanical and Industrial Engineering, University of

More information

ANALYSIS OF STRAY GRAIN FORMATION IN SINGLE-CRYSTAL NICKEL-BASED SUPERALLOY WELDS

ANALYSIS OF STRAY GRAIN FORMATION IN SINGLE-CRYSTAL NICKEL-BASED SUPERALLOY WELDS Superalloys 2004 Edited by K.A. Green, T.M. Pollock, H. Harada, T.E. Howson, R.C. Reed, J.J. Schirra, and S, Walston TMS (The Minerals, Metals & Materials Society), 2004 ANALYSIS OF STRAY GRAIN FORMATION

More information

PHASE EQUILIBRIUM P + F = C + 2

PHASE EQUILIBRIUM P + F = C + 2 PHASE EQUILIBRIUM Component: is either pure metal and/or compound of which an alloy is composed. They refer to the independent chemical species that comprise the system. Solid Solution: It consists of

More information

J = D C A C B x A x B + D C A C. = x A kg /m 2

J = D C A C B x A x B + D C A C. = x A kg /m 2 1. (a) Compare interstitial and vacancy atomic mechanisms for diffusion. (b) Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion. (a) With vacancy diffusion, atomic

More information

Modelling Columnar and Equiaxed Growth. David J. Browne, B.E., M.Sc. St. Anne's College, Oxford

Modelling Columnar and Equiaxed Growth. David J. Browne, B.E., M.Sc. St. Anne's College, Oxford Modelling Columnar and Equiaxed Growth David J. Browne, B.E., M.Sc. St. Anne's College, Oxford A thesis submitted for the degree of Doctor of Philosophy in the University of Oxford Department of Materials

More information

ThermoCalc Application for the Assessment of Binary Alloys Non-Equilibrium Solidification

ThermoCalc Application for the Assessment of Binary Alloys Non-Equilibrium Solidification A R C H I V E S of F O U N D R Y E N G I N E E R I N G Published quarterly as the organ of the Foundry Commission of the Polish Academy of Sciences ISSN (1897-331) Volume 17 Issue 1/217 163 168 3/1 ThermoCalc

More information

MODEL OF GROWTH A IRREGULAR EUTECTICS COMPOSITE IN SITU (MMCs)

MODEL OF GROWTH A IRREGULAR EUTECTICS COMPOSITE IN SITU (MMCs) MODEL OF GROWTH A IRREGULAR EUTECTIC COMPOITE IN ITU (MMCs) Edward Guzik Faculty of Foundry Engineering, University of Mining and Metallurgy, Reymonta 3 treet, 3-59 Kraków, Poland UMMARY: In the part comprising

More information

METALLURGICAL SILICON REFINING BY TRANSIENT DIRECTIONAL SOLIDIFICATION

METALLURGICAL SILICON REFINING BY TRANSIENT DIRECTIONAL SOLIDIFICATION METALLURGICAL SILICON REFINING BY TRANSIENT DIRECTIONAL SOLIDIFICATION Moyses L. LIMA 1,2, Marcelo A. MARTORANO 2, João B. F. NETO 1 1 Laboratory of Metallurgical Processes - Institute for Technological

More information

Continuous Rheocasting for Aluminum-Copper Alloys

Continuous Rheocasting for Aluminum-Copper Alloys Materials Transactions, Vol. 43, No. 9 (2002) pp. 2285 to 2291 c 2002 The Japan Institute of Metals Continuous Rheocasting for Aluminum-Copper Alloys Kiyoshi Ichikawa, Masahito Katoh and Fumio Asuke Ecology-Oriented

More information

Numerical Simulation of Solidification Structure Formation during Continuous Casting in Fe 0.7mass%C Alloy Using Cellular Automaton Method

Numerical Simulation of Solidification Structure Formation during Continuous Casting in Fe 0.7mass%C Alloy Using Cellular Automaton Method , pp. 903 908 Numerical Simulation of Solidification Structure Formation during Continuous Casting in Fe 0.7mass%C Alloy Using Cellular Automaton Method Minoru YAMAZAKI, 1) Yukinobu NATSUME, 1) Hiroshi

More information

Module 29. Precipitation from solid solution I. Lecture 29. Precipitation from solid solution I

Module 29. Precipitation from solid solution I. Lecture 29. Precipitation from solid solution I Module 29 Precipitation from solid solution I Lecture 29 Precipitation from solid solution I 1 Keywords : Properties of two phase alloys, super saturated solid solutions, historical perspective, solution

More information

MME292 Metallic Materials Sessional

MME292 Metallic Materials Sessional Department of Materials and Metallurgical Engineering angladesh University of Engineering and Technology, Dhaka MME292 Metallic Materials Sessional July 2016 Term Experiment 2 Construction and Interpretation

More information

Slide 1. Slide 2. Slide 3. Chapter 10: Solid Solutions and Phase Equilibrium. Learning Objectives. Introduction

Slide 1. Slide 2. Slide 3. Chapter 10: Solid Solutions and Phase Equilibrium. Learning Objectives. Introduction Slide 1 Chapter 10: Solid Solutions and Phase Equilibrium 10-1 Slide 2 Learning Objectives 1. Phases and the phase diagram 2. Solubility and solid solutions 3. Conditions for unlimited solid solubility

More information

PART II: Metal Casting Processes and Equipment

PART II: Metal Casting Processes and Equipment Manufacturing Engineering Technology in SI Units, 6 th Edition PART II: Metal Casting Processes and Equipment Introduction Casting involves pouring molten metal into a mold cavity Process produce intricate

More information

TERNARY PHASE DIAGRAMS

TERNARY PHASE DIAGRAMS TERNARY PHASE DIAGRAMS An Introduction Guna Selvaduray San Jose State University Credit for Phase Diagram Drawings: Richard Brindos Credit for scanning the phase diagrams: Brenden Croom G. Selvaduray -

More information

In this work, the dendrite growth velocity of tetragonal Ni 2 B was measured as a

In this work, the dendrite growth velocity of tetragonal Ni 2 B was measured as a Summary In this work, the dendrite growth velocity of tetragonal Ni 2 B was measured as a function of undercooling under different convective flow conditions to critically asses the effect of fluid flow

More information

Components The elements or compounds which are mixed initially. (e.g. Al & Cu)

Components The elements or compounds which are mixed initially. (e.g. Al & Cu) Why Study Phase Diagrams? The purpose of this lecture is to develop an understanding of the phase transformations which occur under conditions of slow cooling; Under such conditions equilibrium is approached,

More information

Product Data Sheet MCP 137/Metspec 281 Alloy UPDATED ON

Product Data Sheet MCP 137/Metspec 281 Alloy UPDATED ON TYPICAL USES The principal uses of the alloy depend on the density difference between liquid and solid and the dimensional changes after solidification being both very small, the actual magnitude of the

More information

Diffusion phenomenon

Diffusion phenomenon Module-5 Diffusion Contents 1) Diffusion mechanisms and steady-state & non-steady-state diffusion 2) Factors that influence diffusion and nonequilibrium transformation & microstructure Diffusion phenomenon

More information

Solidification and Crystallisation 5. Formation of and control of granular structure

Solidification and Crystallisation 5. Formation of and control of granular structure MME 345 Lecture 08 Solidification and Crystallisation 5. Formation of and control of granular structure Ref: [1] A. Ohno, The Solidification of Metals, Chijin Shokan Co. Ltd., 1976 [2] P. Beeley, Foundry

More information

Segregation and Microstructure in Continuous Casting Shell

Segregation and Microstructure in Continuous Casting Shell Segregation and Microstructure in Continuous Casting Shell Brian G. Thomas and Young-Mok Won Department of Mechanical & Industrial Engineering University of Illinois at Urbana-Champaign September 25, 2000

More information

Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Phase Diagram

Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Phase Diagram SE104 Structural Materials Phase Diagram Dr. Yu Qiao Department of Structural Engineering, UCSD Introduction Phase: A region in a material that differs in structure and function from other regions. Phase

More information

CHAPTER 10 PHASE DIAGRAMS PROBLEM SOLUTIONS

CHAPTER 10 PHASE DIAGRAMS PROBLEM SOLUTIONS CHAPTER 10 PHASE DIAGRAMS PROBLEM SOLUTIONS Solubility Limit 10.1 Consider the sugar water phase diagram of Figure 10.1. (a) How much sugar will dissolve in 1000 g of water at 80 C (176 F)? (b) If the

More information

Part III : Nucleation and growth. Module 4 : Growth of precipitates and kinetics of nucleation and growth. 4.1 Motivating question/phenomenon

Part III : Nucleation and growth. Module 4 : Growth of precipitates and kinetics of nucleation and growth. 4.1 Motivating question/phenomenon Part III : Nucleation and growth Module 4 : Growth of precipitates and kinetics of nucleation and growth 4.1 Motivating question/phenomenon In Figure. 20 we show, schematically, a morphology of precipitates

More information

Phase diagrams. R.D.Makwana,IT,NU. R.D.Makwana,IT,NU

Phase diagrams. R.D.Makwana,IT,NU. R.D.Makwana,IT,NU Phase diagrams Phase?? Phase is region throughout which all properties of material are essentially uniform Uniform region of a system which has uniform physical and chemical characteristics Phase diagram?

More information

Analysis of Yield Rate in Single Crystal Casting Process Using an Engineering Simulation Model

Analysis of Yield Rate in Single Crystal Casting Process Using an Engineering Simulation Model Materials Transactions, Vol. 44, No. 5 (23) pp. 829 to 835 Special Issue on Solidification Science and Processing for Advanced Materials #23 The Japan Institute of Metals Analysis of Yield Rate in Single

More information

1. Introduction. Alexandre Furtado Ferreira a *, Ivaldo Leão Ferreira a, Janaan Pereira da Cunha a, Ingrid Meirelles Salvino a

1. Introduction. Alexandre Furtado Ferreira a *, Ivaldo Leão Ferreira a, Janaan Pereira da Cunha a, Ingrid Meirelles Salvino a Materials Research. 2015; 18(3): 644-653 2015 DOI: http://dx.doi.org/10.1590/1516-1439.293514 Simulation of the Microstructural Evolution of Pure Material and Alloys in an Undercooled Melts via Phase-field

More information

FILLING SIMULATION OF TILT CASTING DÁNIEL MOLNÁR 1

FILLING SIMULATION OF TILT CASTING DÁNIEL MOLNÁR 1 Materials Science and Engineering, Volume 42, No. 1 (2017), pp. 94 101. FILLING SIMULATION OF TILT CASTING DÁNIEL MOLNÁR 1 Reliable fluidity data for commercial aluminium foundry alloys are not readily

More information

Micro-Segregation along the Monovariant Line in a Ternary Eutectic Alloy System

Micro-Segregation along the Monovariant Line in a Ternary Eutectic Alloy System Materials Transactions, Vol. 44, No. 5 (23) pp. 8 to 88 Special Issue on Solidification Science Processing for Advanced Materials #23 The Japan Institute of Metals Micro-Segregation along the Monovariant

More information

Solidification of Metals in Molds

Solidification of Metals in Molds Metal Casting Solidification of Metals in Molds Pure Metals - Solidify at a constant temperature Planar solidification front Columnar crystals Eutectics - Solidify at a constant temperature Planar solidification

More information

Phase Transformation in Materials

Phase Transformation in Materials 2015 Fall Phase Transformation in Materials 09. 23. 2015 Eun Soo Park Office: 33-313 Telephone: 880-7221 Email: espark@snu.ac.kr Office hours: by an appointment 1 - Equilibrium in Heterogeneous Systems

More information

Phase Diagrams, Solid Solutions, Phase Strengthening, Phase Transformations

Phase Diagrams, Solid Solutions, Phase Strengthening, Phase Transformations Phase Diagrams, Solid Solutions, Phase Strengthening, Phase Transformations Components and Phases Components: The elements or compounds that are mixed initially (Al and Cu). Phases: A phase is a homogenous,

More information

Analysis of columnar crystals growth during the solidification in magnetic field J. Szajnar

Analysis of columnar crystals growth during the solidification in magnetic field J. Szajnar Analysis of columnar crystals growth during the solidification in magnetic field J. Szajnar Foundry Institute, Silesian Technical University, 44-10 Gliwice, Towarowa 7, Poland ABSTRACT Interaction of rotational

More information

EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling. Solidification of Silicon. Graham Patrick Benham

EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling. Solidification of Silicon. Graham Patrick Benham EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling Solidification of Silicon Graham Patrick Benham Table of Contents 1. Introduction...2 Background...2 2. Solidification

More information

Schematic representation of the development of microstructure. during the equilibrium solidification of a 35 wt% Ni-65 wt% Cu alloy

Schematic representation of the development of microstructure. during the equilibrium solidification of a 35 wt% Ni-65 wt% Cu alloy Schematic representation of the development of microstructure during the equilibrium solidification of a 35 wt% Ni-65 wt% Cu alloy At 1300 ºC (point a) the alloy is in the liquid condition This continues

More information

Fundamentals of Casting

Fundamentals of Casting Fundamentals of Casting Chapter 11 11.1 Introduction Products go through a series of processes before they are produced Design Material selection Process selection Manufacture Inspection and evaluation

More information

CHAPTER 12. Phase Transformations

CHAPTER 12. Phase Transformations CHAPTER 12 Phase Transformations Introduction Basic concepts The kinetics of phase transformations Metastable versus equilibrium states Isothermal transformation diagrams Continuous cooling transformation

More information

Material Science. Prof. Satish V. Kailas Associate Professor Dept. of Mechanical Engineering, Indian Institute of Science, Bangalore India

Material Science. Prof. Satish V. Kailas Associate Professor Dept. of Mechanical Engineering, Indian Institute of Science, Bangalore India Material Science Prof. Satish V. Kailas Associate Professor Dept. of Mechanical Engineering, Indian Institute of Science, Bangalore 560012 India Chapter 6. Phase Diagrams Learning objectives: - To understand

More information

Phase Diagrams & Phase Tranformation

Phase Diagrams & Phase Tranformation ep-16 Phase Diagrams & Phase Tranformation Microstructure - Phases Ferrite Cementite EM micrograph x magnification Plain C steel containing.44 wt. % C Basic Definitions Alloy: A metallic substance that

More information

Low-frequency Electromagnetic Casting

Low-frequency Electromagnetic Casting University of Ljubljana Faculty of Mathematics and Physics Final Year Seminar Low-frequency Electromagnetic Casting Author: Uroš Žunkovič Mentor: Prof. Dr. Janez Dolinšek Abstract In the last decade, low-frequency

More information

Simulation of High Pressure Die Casting (HPDC) via STAR-Cast

Simulation of High Pressure Die Casting (HPDC) via STAR-Cast Simulation of High Pressure Die Casting (HPDC) via STAR-Cast STAR Global Conf. 2012, 19-21 March, Noordwijk Romuald Laqua, Access e.v., Aachen High Pressure Die Casting: Machines and Products Common Materials:

More information

Part IV : Solid-Solid Phase Transformations I Module 2 : Cellular precipitation

Part IV : Solid-Solid Phase Transformations I Module 2 : Cellular precipitation Part IV : Solid-Solid Phase Transformations I Module 2 : Cellular precipitation 2. Cellular precipitation 2.1 Motivation Consider the microstructure (schematic) shown in Fig. 18. This is a typical microstructure

More information