Uploaded bySumitRathod36
PDF, PPTX539 views

Phase diagram part 2

The document summarizes key concepts regarding binary eutectic systems using copper-silver as an example system. It defines terms like eutectic mixture, eutectic reaction, invariant point, liquidus line, solidus line, and solvus line. The copper-silver phase diagram is used to illustrate these concepts, including that at the eutectic point of 71.9% Cu and 779°C, the liquid transforms into solid copper and silver phases upon cooling in a eutectic reaction.

Embed presentation

Download as PDF, PPTX
PHASE DIAGRAM (Part – 2/3) Prepared by VISHAL MEHTA Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr
CONTENTS Eutectic Mixture Binary Eutectic System Eutectoid Reaction Peritectic Reaction Basic Comparison Congruent Phase Transformation The Gibbs Phase Rule Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 2
EUTECTIC MIXTURE A eutectic mixture is defined as a mixture of two or more components which usually do not interact to form a new chemical compound but, which at certain ratios, inhibit the crystallization process of one another resulting in a system having a lower melting point than either of the components Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 3
EUTECTIC MIXTURE A eutectic mixture is defined as a mixture of two or more components which usually do not interact to form a new chemical compound but, which at certain ratios, inhibit the crystallization process of one another resulting in a system having a lower melting point than either of the components Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 4 Component 1 Melting Temp T1
EUTECTIC MIXTURE A eutectic mixture is defined as a mixture of two or more components which usually do not interact to form a new chemical compound but, which at certain ratios, inhibit the crystallization process of one another resulting in a system having a lower melting point than either of the components Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 5 Component 1 Melting Temp T1 Component 2 Melting Temp T2
EUTECTIC MIXTURE A eutectic mixture is defined as a mixture of two or more components which usually do not interact to form a new chemical compound but, which at certain ratios, inhibit the crystallization process of one another resulting in a system having a lower melting point than either of the components Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 6 Component 1 Melting Temp T1 Component 2 Melting Temp T2 Eutectic Mixture of component 1&2 Melting Temp T12
EUTECTIC MIXTURE A eutectic mixture is defined as a mixture of two or more components which usually do not interact to form a new chemical compound but, which at certain ratios, inhibit the crystallization process of one another resulting in a system having a lower melting point than either of the components Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 7 Component 1 Melting Temp T1 Component 2 Melting Temp T2 Eutectic Mixture of component 1&2 Melting Temp T12 T12 < T1 & T12 < T2
BINARY EUTECTIC SYSTEM •To understand binary eutectic system, example of copper-silver system is considered. •The phase diagram of the copper–silver system is common and relatively simple phase diagram found for binary alloys. •This is known as a binary eutectic phase diagram. •A number of features of this phase diagram are important and worth noting. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 8
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 9 BINARY EUTECTIC SYSTEM
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 10 BINARY EUTECTIC SYSTEM Three single-phase regions are found.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 11 BINARY EUTECTIC SYSTEM Three single-phase regions are found. 𝜶
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 12 BINARY EUTECTIC SYSTEM Three single-phase regions are found. 𝜶 𝜷
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 13 BINARY EUTECTIC SYSTEM Three single-phase regions are found. 𝜶 𝜷 𝑳𝒊𝒒𝒖𝒊𝒅
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 14 BINARY EUTECTIC SYSTEM The phase is a solid solution rich in copper; it has silver as the solute component and an FCC crystal structure.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 15 BINARY EUTECTIC SYSTEM The β phase is a solid solution rich in silver; it has copper as the solute component and an FCC crystal structure.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 16 BINARY EUTECTIC SYSTEM Pure copper and pure silver are also considered to be and β phases, respectively.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 17 BINARY EUTECTIC SYSTEM Three two-phase regions are found.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 18 BINARY EUTECTIC SYSTEM Three two-phase regions are found. 𝜶 + 𝑳
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 19 BINARY EUTECTIC SYSTEM Three two-phase regions are found. 𝜶 + 𝑳 𝜷 + 𝑳
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 20 BINARY EUTECTIC SYSTEM Three two-phase regions are found. 𝜶 + 𝑳 𝜷 + 𝑳 𝜶 + 𝜷
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 21 BINARY EUTECTIC SYSTEM • The solid solubility limit line separating single solid phase region & two solid phase region is termed as SOLVUS LINE. • Here CB & HG are solvus lines. SOLVUS LINE
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 22 BINARY EUTECTIC SYSTEM • The solubility limit line separating single solid phase region & two phase solid+liquid region is termed as SOLIDUS LINE. • Here BA & GF are solidus lines. SOLIDUS LINE
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 23 BINARY EUTECTIC SYSTEM Horizontal isotherm line BEG may also be considered a solidus line; it represents the lowest temperature at which a liquid phase may exist for any copper–silver alloy that is at equilibrium.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 24 BINARY EUTECTIC SYSTEM • The solubility limit line separating single liquid phase region & two phase solid+liquid region is termed as LIQUIDUS LINE. • Here AE & EF are liquidus lines. LIQUIDUS LINE
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 25 BINARY EUTECTIC SYSTEM 1085°C is Melting temperature of Cu As silver is added to copper, the temperature at which the alloys become totally liquid decreases along the liquidus line, line AE; thus, the melting temperature of copper is lowered by silver additions.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 26 BINARY EUTECTIC SYSTEM 961.8°C is Melting temperature of Ag As copper is added to silver, the temperature at which the alloys become totally liquid decreases along the liquidus line, line EF; thus, the melting temperature of silver is lowered by copper additions.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 27 BINARY EUTECTIC SYSTEM • Both liquidus lines meet at the point E on the phase diagram, through which also passes the horizontal isotherm line BEG. Point E is called an invariant point, which is designated by the composition CE & temperature TE E is invariant point
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 28 BINARY EUTECTIC SYSTEM • Both liquidus lines meet at the point E on the phase diagram, through which also passes the horizontal isotherm line BEG. Point E is called an invariant point, which is designated by the composition CE & temperature TE • For the copper–silver system, • CE is 71.9 wt% • TE is 779°C
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 29 BINARY EUTECTIC SYSTEM • For an alloy of composition CE, upon cooling, liquid phase is transformed into two solid phases & β at temperature TE • The opposite reaction occurs upon heating. • This is called a eutectic reaction (eutectic means easily melted) • Horizontal solidus line at TE is called eutectic isotherm Eutectic isotherm
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 30 BINARY EUTECTIC SYSTEM • Eutectics Reaction • TE is eutectic temperature • CE is eutectic composition • C E is eutectic composition of at TE • CβE is eutectic composition of β at TE Eutectic isotherm
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 31 BINARY EUTECTIC SYSTEM • Eutectics Reaction for copper-silver system
EXAMPLE PROBLEM •For a 40 wt% Sn–60 wt% Pb alloy at 150oC (300F), •(1) What phase(s) is (are) present? •(2) What is (are) the composition(s) of the phase(s)? •(3) Calculate the relative amount of each phase present in terms of mass fraction and (b) volume fraction. •(4) Calculate the relative amount of each phase present in terms of volume fraction. •Take the densities of Pb and Sn to be 11.23 and 7.24 g/cm3, respectively. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 32
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 33 Sn-Pb system Obtain point B which represent 40 wt% Sn– 60 wt% Pb alloy at 150oC (300F)
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 34 Sn-Pb system Answer (1) Obtained point is in +β region, both & β phases will Coexist.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 35 Answer (2) Since two phases are present, it becomes necessary to construct a tie line through point B
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 36 Answer (2) 𝑆𝑜, 𝐶𝛼 𝑖𝑠 10 wt% Sn– 90 wt% Pb & 𝐶𝛽 𝑖𝑠 98 wt%Sn– 2 wt% Pb
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 37 Answer (3) Since the alloy consists of two phases, it is necessary to employ the lever rule. One can observe C ,Cβ & C1 in diagram.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 38 Answer (3) So mass fraction of phase is, 𝑊 𝛼 = 𝐶𝛽 − 𝐶1 𝐶𝛽 − 𝐶𝛼 = 98 − 40 98 − 10 = 0.66
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 39 Answer (3) So mass fraction of β phase is, 𝑊𝛽 = 𝐶1 − 𝐶𝛼 𝐶𝛽 − 𝐶𝛼 = 40 − 10 98 − 10 = 0.34
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 40 Answer (4) Volume fractions of phase & β phase are, 𝑽𝜶 = 𝑾𝜶 𝝆𝜶 𝑾𝜶 𝝆𝜶 + 𝑾𝜷 𝝆𝜷 𝑽𝜷 = 𝑾𝜷 𝝆𝜷 𝑾𝜶 𝝆𝜶 + 𝑾𝜷 𝝆𝜷 But we don’t have values of 𝝆𝜶 & 𝝆𝜷
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 41 𝜌𝛼 = 100 𝐶𝑆𝑛(𝛼) 𝜌𝑆𝑛 + 𝐶𝑃𝑏(𝛼) 𝜌𝑃𝑏 = 100 10 7.24𝑔/𝑐𝑚3 + 90 11.23𝑔/𝑐𝑚3 = 10.64 𝑔/𝑐𝑚3 𝜌𝛽 = 100 𝐶𝑆𝑛(𝛽) 𝜌𝑆𝑛 + 𝐶𝑃𝑏(𝛽) 𝜌𝑃𝑏 = 100 98 7.24𝑔/𝑐𝑚3 + 2 11.23𝑔/𝑐𝑚3 = 7.29 𝑔/𝑐𝑚3 (values of 𝜌𝑆𝑛 & 𝜌𝑃𝑏 are given in question) Answer (4)
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 42 Answer (4) 𝑽𝜶 = 𝑾𝜶 𝝆𝜶 𝑾𝜶 𝝆𝜶 + 𝑾𝜷 𝝆𝜷 = 𝟎. 𝟔𝟔 𝟏𝟎. 𝟔𝟒 𝒈/𝒄𝒎𝟑 𝟎. 𝟔𝟔 𝟏𝟎. 𝟔𝟒 𝒈/𝒄𝒎𝟑 + 𝟎. 𝟑𝟒 𝟕. 𝟐𝟗 𝒈/𝒄𝒎𝟑 ∴ 𝑽𝜶= 𝟎. 𝟓𝟕
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 43 Answer (4) 𝑽𝜷 = 𝑾𝜷 𝝆𝜷 𝑾𝜶 𝝆𝜶 + 𝑾𝜷 𝝆𝜷 = 𝟎. 𝟑𝟒 𝟕. 𝟐𝟗 𝒈/𝒄𝒎𝟑 𝟎. 𝟔𝟔 𝟏𝟎. 𝟔𝟒 𝒈/𝒄𝒎𝟑 + 𝟎. 𝟑𝟒 𝟕. 𝟐𝟗 𝒈/𝒄𝒎𝟑 ∴ 𝑽𝜶= 𝟎. 𝟒𝟑
• One can also obtaine answer (3) & (4) using following relations. • So just find one value & other is obtained from this relation. • One can observe the answers, which obtained previously Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 44 𝑾𝜶 + 𝑾𝜷 = 𝟏 𝑽𝜶 + 𝑽𝜷 = 𝟏 𝑾𝜶 = 𝟎. 𝟔𝟔 𝑽𝜶 = 𝟎. 𝟓𝟕 𝑾𝜷 = 𝟎. 𝟑𝟒 𝑽𝜷 = 𝟎. 𝟒𝟑 𝟎. 𝟔𝟔 + 𝟎. 𝟑𝟒 = 𝟏 𝟎. 𝟓𝟕 + 𝟎. 𝟒𝟑 = 𝟏
EUTECTOID REACTION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 45 When there is a transformation form one solid phase to two other solid phases or reverse is called Eutectoid Reaction. Cu-Zn system
EUTECTOID REACTION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 46 In simple words, one can under stand that Upon cooling, a solid phase transforms into two other solid phases ( γ and є ). And the reverse reaction occurs upon heating. It is called Eutectic Reaction Cu-Zn system
EUTECTOID REACTION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 47 In simple words, one can under stand that Upon cooling, a solid phase transforms into two other solid phases ( γ and є ). And the reverse reaction occurs upon heating. It is called Eutectic Reaction Cu-Zn system
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 48 Cu-Zn system
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 49 Cu-Zn system
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 50 Cu-Zn system Eutectoid Reaction
PERITECTIC REACTION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 51 When there is a transformation form solid & liquid phase to other different solid phase or reverse is called Peritectic Reaction. Cu-Zn system
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 52 In simple words, one can under stand that Upon cooling, a + L phase transforms into two other solid phase є. And the reverse reaction occurs upon heating. It is called Peritectic Reaction Cu-Zn system PERITECTIC REACTION
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 53 Cu-Zn system PERITECTIC REACTION In simple words, one can under stand that Upon cooling, a + L phase transforms into two other solid phase є. And the reverse reaction occurs upon heating. It is called Peritectic Reaction
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 54 Cu-Zn system
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 55 Cu-Zn system
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 56 Cu-Zn system Peritectic Reaction
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 57 Which one is Eutectic Reaction ? What is Eutectic Reaction?
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 58 Which one is Eutectic Reaction ? What is Eutectic Reaction?
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 59 Which one is Eutectic Reaction ? What is Eutectic Reaction? Which one is Eutectoid Reaction ? What is Eutectoid Reaction? How to identify the Reaction ?
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 60 Which one is Eutectic Reaction ? What is Eutectic Reaction? Which one is Eutectoid Reaction ? What is Eutectoid Reaction? Which one is Peritectic Reaction ? What is Peritectic Reaction? How to identify the Reaction ?
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 61 Which one is Eutectic Reaction ? What is Eutectic Reaction? Which one is Eutectoid Reaction ? What is Eutectoid Reaction? Which one is Peritectic Reaction ? What is Peritectic Reaction? How to identify the Reaction ?
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 62 Which one is Eutectic Reaction ? What is Eutectic Reaction? Which one is Eutectoid Reaction ? What is Eutectoid Reaction? Which one is Peritectic Reaction ? What is Peritectic Reaction? How to identify the Reaction ? Confused ?
BASIC COMPARISION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 63 EUTECTIC REACTION EUTECTOID REACTION PERITECTIC REACTION Liquid phase Type-1 solid phase Type-2 solid phase Type-1 solid phase Type-2 solid phase Type-3 solid phase Type-1 solid phase Liquid phase Type-2 solid phase Note : There is no specific meaning of type 1, 2 & 3. It is just randomly used to differentiate the solid phases.
CONGRUENT PHASE TRANSFORMATION •Phase transformations may be classified according to whether or not there is any change in composition for the phases involved. •Those for which there are no compositional alterations are said to be congruent transformations. •It means phase changes without any change in wt% composition. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 64
CONGRUENT PHASE TRANSFORMATION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 65 Type – 1 phase with composition X wt% metal A Y wt% metal B
CONGRUENT PHASE TRANSFORMATION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 66 Type – 1 phase with composition X wt% metal A Y wt% metal B Congruent Phase Transformation
CONGRUENT PHASE TRANSFORMATION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 67 Type – 1 phase with composition X wt% metal A Y wt% metal B Type – 2 phase with same composition X wt% metal A Y wt% metal B Congruent Phase Transformation
CONGRUENT PHASE TRANSFORMATION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 68 A portion of the nickel–titanium phase diagram on which is shown a congruent melting point for the γ - phase solid solution at 1310OC and 44.9 wt% Ti.
CONGRUENT PHASE TRANSFORMATION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 69 A portion of the nickel–titanium phase diagram on which is shown a congruent melting point for the γ - phase solid solution at 1310OC and 44.9 wt% Ti.
CONGRUENT PHASE TRANSFORMATION Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 70 A portion of the nickel–titanium phase diagram on which is shown a congruent melting point for the γ - phase solid solution at 1310OC and 44.9 wt% Ti. Congruent Phase Transformation L γ
THE GIBBS PHASE RULE Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 71 Josiah Willard Gibbs the nineteenth-century physicist
THE GIBBS PHASE RULE Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 72 Josiah Willard Gibbs the nineteenth-century physicist
THE GIBBS PHASE RULE P + F = C + N P = number of phases present F = number of degrees of freedom or the number of externally controlled variables (e.g., temperature, pressure, composition) C = number of components in the system N = number of noncompositional variables (e.g., temperature and pressure) • This rule represents a criterion for the number of phases that will coexist within a system at equilibrium Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 73 Josiah Willard Gibbs the nineteenth-century physicist
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 74 THE GIBBS PHASE RULE Continue…
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 75 THE GIBBS PHASE RULE Continue… Consider that we want to find the number of degrees of freedom or the number of externally controlled variables for the single phase field of Cu-Ag system
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 76 THE GIBBS PHASE RULE Continue… • Now Gibbs phase rule is P + F = C + N • Here • P = number of phases present • As we have considered single phase field, P = 1 • F = ? • C = number of components in system • As it is binary system, C = 2 • N = number of noncompositional variables (e.g., temperature and pressure) • Here we need to check that temperature & pressure are variable or not. • If both are variable, N = 2. If any one of two is variable, N = 1.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 77 THE GIBBS PHASE RULE Continue… • It has been discussed in initial phase of this chapter that for binary system Temperature and composition are variable parameters, and pressure is held constant—normally 1 atm. (slide no 17 & 24 of Part-1) • So here only temperature is variable, N = 1. • Gibbs phase rule is P + F = C + N • So 1 + F = 2 + 1 • F = 2
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 78 THE GIBBS PHASE RULE Continue… • What is the meaning of F = 2 ? • This means that to completely describe the characteristics of any alloy that exists within one of these phase fields, we must specify two parameters; these are composition and temperature, which locate, respectively, the horizontal and vertical positions of the alloy on the phase diagram.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 79 meaning of F = 2 • In other words, it can be said that one can vary two parameters. • It means for any value of T, you may get more than one values of C & vice versa.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 80 THE GIBBS PHASE RULE Continue… • Now for the same example & same system, consider two phase field (instead of single phase). • So, P = 2 • Gibbs phase rule is P + F = C + N • So 2 + F = 2 + 1 • F = 1
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 81 THE GIBBS PHASE RULE Continue… • What is the meaning of F = 1 ? • F = 1 means it is necessary to specify either temperature or the composition of one of the phases to completely define the system.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 82 meaning of F = 1 • Number of variable parameter is 1 • So, if you know any one value of three, remaining two values you can find. • For example if you know T1, you will get other two values of C & Cβ. • Or if you know C , you can find other two values.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 83 meaning of F = 1 • In other words, it can be said that one can vary only one parameter and other two will be changed. • It means for any value of T1, you will get one specific value of C & one specific value of Cβ. • (point can be any where on tie line/isotherm)
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 84 THE GIBBS PHASE RULE Continue… • Now for the same example & same system, consider three phase field (instead of two phase). • So, P = 3 • Gibbs phase rule is P + F = C + N • So 3 + F = 2 + 1 • F = 0
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 85 THE GIBBS PHASE RULE Continue… • What is the meaning of F = 0 ? • This means that the compositions of all three phases as well as the temperature are fixed.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 86 meaning of F = 0 • Number of variable parameter is 0. • It means values of T, CL, C & Cβ are fixed.
Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 87 END OF PART – 2 …. PLEASE CHECK PART – 3 ….

More Related Content

PDF
Phase diagram part 1
bySumitRathod36
 
PPTX
Stress crack phenomena in austenitic grade stainless steel
byKoushik Kosanam
 
PPT
Iron making
byguddu_92
 
PPT
Material Science Chapter 4
byamzar17
 
PPTX
fe-c diagram
bySMALL ARMS FACTORY (MINISTRY OF DEFENSE)
 
PDF
6 phase and phase equilibrium chapter
byNaman Dave
 
PPTX
Ti final
byDeepansha Kakkar
 
PPTX
MODULE - 1 : ELECTROCHEMISTRY
byrashmi m rashmi
 
Phase diagram part 1
bySumitRathod36
 
Stress crack phenomena in austenitic grade stainless steel
byKoushik Kosanam
 
Iron making
byguddu_92
 
Material Science Chapter 4
byamzar17
 
fe-c diagram
bySMALL ARMS FACTORY (MINISTRY OF DEFENSE)
 
6 phase and phase equilibrium chapter
byNaman Dave
 
Ti final
byDeepansha Kakkar
 
MODULE - 1 : ELECTROCHEMISTRY
byrashmi m rashmi
 

What's hot

PDF
1 intro & history
bySuraj Aggarwal
 
PPT
Iron carbon diagram
byRahul Sen
 
PPTX
Crystallographic planes and directions
byNicola Ergo
 
PPTX
Dynamic mechanical analysis (DMA)
byBijay Kumar
 
PPTX
Impact test
byhafizarsalan3
 
PPS
ASTM E 112 GRAIN SIZE MEASURING METHODS full standard, mecanical
byJeet Amrutiya
 
PPTX
mechanical models of polymer behavior
byTayyaba Khalid
 
PPT
Ch10
byIbrahim Abuawwad
 
PPT
phase diagrams
byNurul Adni
 
PPTX
Dr.R.Narayanasamy - Super Plasticity
byDr.Ramaswamy Narayanasamy
 
PPTX
Crystal defects
byBIPIN KUMAR MISHRA
 
PPTX
Steel and effect of alloying elements
bytemkin abdlkader
 
PPT
CHAPTER 5 behavior of polymers XX.ppt
byTESFAYE Weldebrhan Hadush
 
PPTX
Crystal growth techniques
bySHASHI SHAW
 
PPTX
Cast irons
bytemkin abdlkader
 
PDF
Molecular weight of Polymer
byHaseeb Ahmad
 
PPT
Voids in crystals
byMaramandansubu
 
PPTX
Iron Carbon Equilibrium Diagram
byAditi Rana
 
PPTX
Steel
byGulfam Hussain
 
PPTX
nucleation and methods to control grain structure
byChintan Mehta
 
1 intro & history
bySuraj Aggarwal
 
Iron carbon diagram
byRahul Sen
 
Crystallographic planes and directions
byNicola Ergo
 
Dynamic mechanical analysis (DMA)
byBijay Kumar
 
Impact test
byhafizarsalan3
 
ASTM E 112 GRAIN SIZE MEASURING METHODS full standard, mecanical
byJeet Amrutiya
 
mechanical models of polymer behavior
byTayyaba Khalid
 
Ch10
byIbrahim Abuawwad
 
phase diagrams
byNurul Adni
 
Dr.R.Narayanasamy - Super Plasticity
byDr.Ramaswamy Narayanasamy
 
Crystal defects
byBIPIN KUMAR MISHRA
 
Steel and effect of alloying elements
bytemkin abdlkader
 
CHAPTER 5 behavior of polymers XX.ppt
byTESFAYE Weldebrhan Hadush
 
Crystal growth techniques
bySHASHI SHAW
 
Cast irons
bytemkin abdlkader
 
Molecular weight of Polymer
byHaseeb Ahmad
 
Voids in crystals
byMaramandansubu
 
Iron Carbon Equilibrium Diagram
byAditi Rana
 
Steel
byGulfam Hussain
 
nucleation and methods to control grain structure
byChintan Mehta
 

Similar to Phase diagram part 2

PPTX
Phase diagrams
bysenthamarai kannan
 
PDF
Chapter 9 phase diagrams 1
byMeelu Qazi
 
PDF
Lecture 8: Phase Diagrams
byUniversity of Liverpool
 
PPTX
Types of phase daigram
byGulfam Hussain
 
PPTX
Phase diagrams
bysaravana kumar
 
PPTX
Two Component System
byManipal Academy of Higher Education (MAHE)
 
PDF
Correlation of the eutectic type alloy with the phase diagram
bySaif al-din ali
 
PPT
Phase diagram (Muda Ibrahim)
byMuda Ibrahim
 
PDF
CHAPTER 9.1 - PHASE DIAGRAMS FOR METALLIC SYSTEMS.pdf
byMuhammadMirwazi
 
PDF
9 - Phase diagrams.pdf
byupender3
 
PPT
10[1].Phase Diagrams.ppt
byVipul Saxena
 
PPTX
EMM - Unit 1.pptx
byvignesh589621
 
PPT
ch10-Phase_Diagramsbsnsbbbsbsbsbbwbwbwb.ppt
byvamshi Kickuuu
 
PPTX
Phase Diagrams (1).pptx Lecture-2 Physical Metallurgy_ Crystal structure (1)....
bybt21108039RajeshKuma
 
PPT
Week 5
byQazi Ali
 
PPT
Ch. 09 Phase Diagrams Material engineering.ppt
bymuhammadahmed909758
 
PPTX
Phase Diagram for different alloy system.pptx
byamitkumarme1
 
PPT
chapter 11 phase diagram. for simple system
byasmasharfeddin
 
PPTX
EM.pptx
byvignesh589621
 
PDF
Ch09 phase diagm-sent-fall2016
bySavanna Holt
 
Phase diagrams
bysenthamarai kannan
 
Chapter 9 phase diagrams 1
byMeelu Qazi
 
Lecture 8: Phase Diagrams
byUniversity of Liverpool
 
Types of phase daigram
byGulfam Hussain
 
Phase diagrams
bysaravana kumar
 
Two Component System
byManipal Academy of Higher Education (MAHE)
 
Correlation of the eutectic type alloy with the phase diagram
bySaif al-din ali
 
Phase diagram (Muda Ibrahim)
byMuda Ibrahim
 
CHAPTER 9.1 - PHASE DIAGRAMS FOR METALLIC SYSTEMS.pdf
byMuhammadMirwazi
 
9 - Phase diagrams.pdf
byupender3
 
10[1].Phase Diagrams.ppt
byVipul Saxena
 
EMM - Unit 1.pptx
byvignesh589621
 
ch10-Phase_Diagramsbsnsbbbsbsbsbbwbwbwb.ppt
byvamshi Kickuuu
 
Phase Diagrams (1).pptx Lecture-2 Physical Metallurgy_ Crystal structure (1)....
bybt21108039RajeshKuma
 
Week 5
byQazi Ali
 
Ch. 09 Phase Diagrams Material engineering.ppt
bymuhammadahmed909758
 
Phase Diagram for different alloy system.pptx
byamitkumarme1
 
chapter 11 phase diagram. for simple system
byasmasharfeddin
 
EM.pptx
byvignesh589621
 
Ch09 phase diagm-sent-fall2016
bySavanna Holt
 

Recently uploaded

PPTX
The Complete Guide to Energy Audits_ Unlocking Savings, Sustainability, and P...
bygreentechnexus2024
 
PDF
chapter 30 inductance chương trình tiên tiến bách khoa.pdf
byconbohai1500
 
PPTX
Introduction to Civil Engineering-Defination, Branches of civil engineering a...
byvidyanand kadam
 
PPTX
Optimizing Plant Maintenance — Key Elements of a Successful Maintenance Plan ...
byMaintWiz Technologies Private Limited
 
PPTX
Optimizing Operations: Key Elements of a Successful Plant Maintenance Plan — ...
byMaintWiz Technologies Private Limited
 
PPTX
KTU 2024 SCHEME -PEMET 413 COMPOSITE MATERIALS MODULE 1 LECTURE 1.pptx
byVinayB68
 
PPTX
Preventive Maintenance Program for Compressors – Complete Guide
byMaintWiz Technologies Private Limited
 
PPTX
How to Create an Effective Monthly Preventive Maintenance Plan
byMaintWiz Technologies Private Limited
 
PPTX
Civil_Engineering_Technician_Skill_Assessment_2025_2026_Presentation.pptx
byCDR Australia Engineer
 
PPTX
Transportation Engineering- Modes of Transport, Types of roads, Components of...
byvidyanand kadam
 
PPTX
22PEOIT4C Session 9 Local search in continuous space.pptx
bymailmegokilavani
 
PPTX
A7383 3D Printing UNIT-III : 3D printing techniques
byVishnuVardhan909561
 
PPTX
UNIT -3 -DIGITAL AND MOBILE FORENSICS FORENSIC READINESS-.pptx
byjemimaa3
 
PPTX
Aix-Marseille Université Diploma
by美国加利福尼亚州立理工大学波莫纳分校学位证书补办【Q微号:1954 292 140】CPP毕业证购买
 
PPTX
22PEOIT4C Session 1 Introduction to AI and intelligent agents.pptx
bymailmegokilavani
 
PDF
Troubleshooting of Marine Refrigeration System - Part 4
byMahmoud Moghtaderi
 
PPTX
Plant Bio-additives (2).pptxA plant bioadditive is a functional substance der...
byMadan Bhandari university and St. Xavier's college , Maitighar
 
PDF
Hybrid Anomaly Detection Mechanism for IOT Networks
byIJCNCJournal
 
PDF
3rd International Conference on AI & Civil Engineering (AICiViL 2025)
byieijjournal
 
PPTX
2_Consequence of threats, E-mail threats, Web.pptx
bydolly475229
 
The Complete Guide to Energy Audits_ Unlocking Savings, Sustainability, and P...
bygreentechnexus2024
 
chapter 30 inductance chương trình tiên tiến bách khoa.pdf
byconbohai1500
 
Introduction to Civil Engineering-Defination, Branches of civil engineering a...
byvidyanand kadam
 
Optimizing Plant Maintenance — Key Elements of a Successful Maintenance Plan ...
byMaintWiz Technologies Private Limited
 
Optimizing Operations: Key Elements of a Successful Plant Maintenance Plan — ...
byMaintWiz Technologies Private Limited
 
KTU 2024 SCHEME -PEMET 413 COMPOSITE MATERIALS MODULE 1 LECTURE 1.pptx
byVinayB68
 
Preventive Maintenance Program for Compressors – Complete Guide
byMaintWiz Technologies Private Limited
 
How to Create an Effective Monthly Preventive Maintenance Plan
byMaintWiz Technologies Private Limited
 
Civil_Engineering_Technician_Skill_Assessment_2025_2026_Presentation.pptx
byCDR Australia Engineer
 
Transportation Engineering- Modes of Transport, Types of roads, Components of...
byvidyanand kadam
 
22PEOIT4C Session 9 Local search in continuous space.pptx
bymailmegokilavani
 
A7383 3D Printing UNIT-III : 3D printing techniques
byVishnuVardhan909561
 
UNIT -3 -DIGITAL AND MOBILE FORENSICS FORENSIC READINESS-.pptx
byjemimaa3
 
Aix-Marseille Université Diploma
by美国加利福尼亚州立理工大学波莫纳分校学位证书补办【Q微号:1954 292 140】CPP毕业证购买
 
22PEOIT4C Session 1 Introduction to AI and intelligent agents.pptx
bymailmegokilavani
 
Troubleshooting of Marine Refrigeration System - Part 4
byMahmoud Moghtaderi
 
Plant Bio-additives (2).pptxA plant bioadditive is a functional substance der...
byMadan Bhandari university and St. Xavier's college , Maitighar
 
Hybrid Anomaly Detection Mechanism for IOT Networks
byIJCNCJournal
 
3rd International Conference on AI & Civil Engineering (AICiViL 2025)
byieijjournal
 
2_Consequence of threats, E-mail threats, Web.pptx
bydolly475229
 
In this document
Powered by AI

Introduction to Phase Diagrams, focusing on Eutectic Systems, Eutectoid and Peritectic Reactions, and essential concepts like Gibbs Phase Rule.

Definition of Eutectic Mixtures, highlighting lower melting points than individual components and their crystallization process.

Explains the Binary Eutectic System, using copper-silver examples, and identifying phases, including liquidus, solidus lines, and E as invariant point.

Problem-solving for Sn-Pb alloy to identify phases, compositions, and calculate mass and volume fractions using phase diagram techniques.

Eutectoid reactions defined as solid phase transformations into two phases; Peritectic reactions involve transformations from solid and liquid into another solid.

Identifying Eutectic, Eutectoid, and Peritectic Reactions; their distinct characteristics and transformation processes.

Basic comparison among Eutectic, Eutectoid, and Peritectic Reactions, distinguishing their characteristics and phase interactions.

Definition of congruent transformations in phase diagrams where no compositional change occurs during phase changes.

Gibbs Phase Rule stated (P + F = C + N) explaining the relationship of phases in a binary system and degrees of freedom.

Phase diagram part 2

  • 1.
    PHASE DIAGRAM (Part –2/3) Prepared by VISHAL MEHTA Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr
  • 2.
    CONTENTS Eutectic Mixture Binary EutecticSystem Eutectoid Reaction Peritectic Reaction Basic Comparison Congruent Phase Transformation The Gibbs Phase Rule Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 2
  • 3.
    EUTECTIC MIXTURE A eutecticmixture is defined as a mixture of two or more components which usually do not interact to form a new chemical compound but, which at certain ratios, inhibit the crystallization process of one another resulting in a system having a lower melting point than either of the components Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 3
  • 4.
    EUTECTIC MIXTURE A eutecticmixture is defined as a mixture of two or more components which usually do not interact to form a new chemical compound but, which at certain ratios, inhibit the crystallization process of one another resulting in a system having a lower melting point than either of the components Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 4 Component 1 Melting Temp T1
  • 5.
    EUTECTIC MIXTURE A eutecticmixture is defined as a mixture of two or more components which usually do not interact to form a new chemical compound but, which at certain ratios, inhibit the crystallization process of one another resulting in a system having a lower melting point than either of the components Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 5 Component 1 Melting Temp T1 Component 2 Melting Temp T2
  • 6.
    EUTECTIC MIXTURE A eutecticmixture is defined as a mixture of two or more components which usually do not interact to form a new chemical compound but, which at certain ratios, inhibit the crystallization process of one another resulting in a system having a lower melting point than either of the components Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 6 Component 1 Melting Temp T1 Component 2 Melting Temp T2 Eutectic Mixture of component 1&2 Melting Temp T12
  • 7.
    EUTECTIC MIXTURE A eutecticmixture is defined as a mixture of two or more components which usually do not interact to form a new chemical compound but, which at certain ratios, inhibit the crystallization process of one another resulting in a system having a lower melting point than either of the components Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 7 Component 1 Melting Temp T1 Component 2 Melting Temp T2 Eutectic Mixture of component 1&2 Melting Temp T12 T12 < T1 & T12 < T2
  • 8.
    BINARY EUTECTIC SYSTEM •Tounderstand binary eutectic system, example of copper-silver system is considered. •The phase diagram of the copper–silver system is common and relatively simple phase diagram found for binary alloys. •This is known as a binary eutectic phase diagram. •A number of features of this phase diagram are important and worth noting. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 8
  • 9.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 9 BINARY EUTECTIC SYSTEM
  • 10.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 10 BINARY EUTECTIC SYSTEM Three single-phase regions are found.
  • 11.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 11 BINARY EUTECTIC SYSTEM Three single-phase regions are found. 𝜶
  • 12.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 12 BINARY EUTECTIC SYSTEM Three single-phase regions are found. 𝜶 𝜷
  • 13.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 13 BINARY EUTECTIC SYSTEM Three single-phase regions are found. 𝜶 𝜷 𝑳𝒊𝒒𝒖𝒊𝒅
  • 14.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 14 BINARY EUTECTIC SYSTEM The phase is a solid solution rich in copper; it has silver as the solute component and an FCC crystal structure.
  • 15.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 15 BINARY EUTECTIC SYSTEM The β phase is a solid solution rich in silver; it has copper as the solute component and an FCC crystal structure.
  • 16.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 16 BINARY EUTECTIC SYSTEM Pure copper and pure silver are also considered to be and β phases, respectively.
  • 17.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 17 BINARY EUTECTIC SYSTEM Three two-phase regions are found.
  • 18.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 18 BINARY EUTECTIC SYSTEM Three two-phase regions are found. 𝜶 + 𝑳
  • 19.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 19 BINARY EUTECTIC SYSTEM Three two-phase regions are found. 𝜶 + 𝑳 𝜷 + 𝑳
  • 20.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 20 BINARY EUTECTIC SYSTEM Three two-phase regions are found. 𝜶 + 𝑳 𝜷 + 𝑳 𝜶 + 𝜷
  • 21.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 21 BINARY EUTECTIC SYSTEM • The solid solubility limit line separating single solid phase region & two solid phase region is termed as SOLVUS LINE. • Here CB & HG are solvus lines. SOLVUS LINE
  • 22.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 22 BINARY EUTECTIC SYSTEM • The solubility limit line separating single solid phase region & two phase solid+liquid region is termed as SOLIDUS LINE. • Here BA & GF are solidus lines. SOLIDUS LINE
  • 23.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 23 BINARY EUTECTIC SYSTEM Horizontal isotherm line BEG may also be considered a solidus line; it represents the lowest temperature at which a liquid phase may exist for any copper–silver alloy that is at equilibrium.
  • 24.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 24 BINARY EUTECTIC SYSTEM • The solubility limit line separating single liquid phase region & two phase solid+liquid region is termed as LIQUIDUS LINE. • Here AE & EF are liquidus lines. LIQUIDUS LINE
  • 25.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 25 BINARY EUTECTIC SYSTEM 1085°C is Melting temperature of Cu As silver is added to copper, the temperature at which the alloys become totally liquid decreases along the liquidus line, line AE; thus, the melting temperature of copper is lowered by silver additions.
  • 26.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 26 BINARY EUTECTIC SYSTEM 961.8°C is Melting temperature of Ag As copper is added to silver, the temperature at which the alloys become totally liquid decreases along the liquidus line, line EF; thus, the melting temperature of silver is lowered by copper additions.
  • 27.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 27 BINARY EUTECTIC SYSTEM • Both liquidus lines meet at the point E on the phase diagram, through which also passes the horizontal isotherm line BEG. Point E is called an invariant point, which is designated by the composition CE & temperature TE E is invariant point
  • 28.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 28 BINARY EUTECTIC SYSTEM • Both liquidus lines meet at the point E on the phase diagram, through which also passes the horizontal isotherm line BEG. Point E is called an invariant point, which is designated by the composition CE & temperature TE • For the copper–silver system, • CE is 71.9 wt% • TE is 779°C
  • 29.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 29 BINARY EUTECTIC SYSTEM • For an alloy of composition CE, upon cooling, liquid phase is transformed into two solid phases & β at temperature TE • The opposite reaction occurs upon heating. • This is called a eutectic reaction (eutectic means easily melted) • Horizontal solidus line at TE is called eutectic isotherm Eutectic isotherm
  • 30.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 30 BINARY EUTECTIC SYSTEM • Eutectics Reaction • TE is eutectic temperature • CE is eutectic composition • C E is eutectic composition of at TE • CβE is eutectic composition of β at TE Eutectic isotherm
  • 31.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 31 BINARY EUTECTIC SYSTEM • Eutectics Reaction for copper-silver system
  • 32.
    EXAMPLE PROBLEM •For a40 wt% Sn–60 wt% Pb alloy at 150oC (300F), •(1) What phase(s) is (are) present? •(2) What is (are) the composition(s) of the phase(s)? •(3) Calculate the relative amount of each phase present in terms of mass fraction and (b) volume fraction. •(4) Calculate the relative amount of each phase present in terms of volume fraction. •Take the densities of Pb and Sn to be 11.23 and 7.24 g/cm3, respectively. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 32
  • 33.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 33 Sn-Pb system Obtain point B which represent 40 wt% Sn– 60 wt% Pb alloy at 150oC (300F)
  • 34.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 34 Sn-Pb system Answer (1) Obtained point is in +β region, both & β phases will Coexist.
  • 35.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 35 Answer (2) Since two phases are present, it becomes necessary to construct a tie line through point B
  • 36.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 36 Answer (2) 𝑆𝑜, 𝐶𝛼 𝑖𝑠 10 wt% Sn– 90 wt% Pb & 𝐶𝛽 𝑖𝑠 98 wt%Sn– 2 wt% Pb
  • 37.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 37 Answer (3) Since the alloy consists of two phases, it is necessary to employ the lever rule. One can observe C ,Cβ & C1 in diagram.
  • 38.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 38 Answer (3) So mass fraction of phase is, 𝑊 𝛼 = 𝐶𝛽 − 𝐶1 𝐶𝛽 − 𝐶𝛼 = 98 − 40 98 − 10 = 0.66
  • 39.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 39 Answer (3) So mass fraction of β phase is, 𝑊𝛽 = 𝐶1 − 𝐶𝛼 𝐶𝛽 − 𝐶𝛼 = 40 − 10 98 − 10 = 0.34
  • 40.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 40 Answer (4) Volume fractions of phase & β phase are, 𝑽𝜶 = 𝑾𝜶 𝝆𝜶 𝑾𝜶 𝝆𝜶 + 𝑾𝜷 𝝆𝜷 𝑽𝜷 = 𝑾𝜷 𝝆𝜷 𝑾𝜶 𝝆𝜶 + 𝑾𝜷 𝝆𝜷 But we don’t have values of 𝝆𝜶 & 𝝆𝜷
  • 41.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 41 𝜌𝛼 = 100 𝐶𝑆𝑛(𝛼) 𝜌𝑆𝑛 + 𝐶𝑃𝑏(𝛼) 𝜌𝑃𝑏 = 100 10 7.24𝑔/𝑐𝑚3 + 90 11.23𝑔/𝑐𝑚3 = 10.64 𝑔/𝑐𝑚3 𝜌𝛽 = 100 𝐶𝑆𝑛(𝛽) 𝜌𝑆𝑛 + 𝐶𝑃𝑏(𝛽) 𝜌𝑃𝑏 = 100 98 7.24𝑔/𝑐𝑚3 + 2 11.23𝑔/𝑐𝑚3 = 7.29 𝑔/𝑐𝑚3 (values of 𝜌𝑆𝑛 & 𝜌𝑃𝑏 are given in question) Answer (4)
  • 42.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 42 Answer (4) 𝑽𝜶 = 𝑾𝜶 𝝆𝜶 𝑾𝜶 𝝆𝜶 + 𝑾𝜷 𝝆𝜷 = 𝟎. 𝟔𝟔 𝟏𝟎. 𝟔𝟒 𝒈/𝒄𝒎𝟑 𝟎. 𝟔𝟔 𝟏𝟎. 𝟔𝟒 𝒈/𝒄𝒎𝟑 + 𝟎. 𝟑𝟒 𝟕. 𝟐𝟗 𝒈/𝒄𝒎𝟑 ∴ 𝑽𝜶= 𝟎. 𝟓𝟕
  • 43.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 43 Answer (4) 𝑽𝜷 = 𝑾𝜷 𝝆𝜷 𝑾𝜶 𝝆𝜶 + 𝑾𝜷 𝝆𝜷 = 𝟎. 𝟑𝟒 𝟕. 𝟐𝟗 𝒈/𝒄𝒎𝟑 𝟎. 𝟔𝟔 𝟏𝟎. 𝟔𝟒 𝒈/𝒄𝒎𝟑 + 𝟎. 𝟑𝟒 𝟕. 𝟐𝟗 𝒈/𝒄𝒎𝟑 ∴ 𝑽𝜶= 𝟎. 𝟒𝟑
  • 44.
    • One canalso obtaine answer (3) & (4) using following relations. • So just find one value & other is obtained from this relation. • One can observe the answers, which obtained previously Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 44 𝑾𝜶 + 𝑾𝜷 = 𝟏 𝑽𝜶 + 𝑽𝜷 = 𝟏 𝑾𝜶 = 𝟎. 𝟔𝟔 𝑽𝜶 = 𝟎. 𝟓𝟕 𝑾𝜷 = 𝟎. 𝟑𝟒 𝑽𝜷 = 𝟎. 𝟒𝟑 𝟎. 𝟔𝟔 + 𝟎. 𝟑𝟒 = 𝟏 𝟎. 𝟓𝟕 + 𝟎. 𝟒𝟑 = 𝟏
  • 45.
    EUTECTOID REACTION Prepared byVISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 45 When there is a transformation form one solid phase to two other solid phases or reverse is called Eutectoid Reaction. Cu-Zn system
  • 46.
    EUTECTOID REACTION Prepared byVISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 46 In simple words, one can under stand that Upon cooling, a solid phase transforms into two other solid phases ( γ and є ). And the reverse reaction occurs upon heating. It is called Eutectic Reaction Cu-Zn system
  • 47.
    EUTECTOID REACTION Prepared byVISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 47 In simple words, one can under stand that Upon cooling, a solid phase transforms into two other solid phases ( γ and є ). And the reverse reaction occurs upon heating. It is called Eutectic Reaction Cu-Zn system
  • 48.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 48 Cu-Zn system
  • 49.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 49 Cu-Zn system
  • 50.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 50 Cu-Zn system Eutectoid Reaction
  • 51.
    PERITECTIC REACTION Prepared byVISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 51 When there is a transformation form solid & liquid phase to other different solid phase or reverse is called Peritectic Reaction. Cu-Zn system
  • 52.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 52 In simple words, one can under stand that Upon cooling, a + L phase transforms into two other solid phase є. And the reverse reaction occurs upon heating. It is called Peritectic Reaction Cu-Zn system PERITECTIC REACTION
  • 53.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 53 Cu-Zn system PERITECTIC REACTION In simple words, one can under stand that Upon cooling, a + L phase transforms into two other solid phase є. And the reverse reaction occurs upon heating. It is called Peritectic Reaction
  • 54.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 54 Cu-Zn system
  • 55.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 55 Cu-Zn system
  • 56.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 56 Cu-Zn system Peritectic Reaction
  • 57.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 57 Which one is Eutectic Reaction ? What is Eutectic Reaction?
  • 58.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 58 Which one is Eutectic Reaction ? What is Eutectic Reaction?
  • 59.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 59 Which one is Eutectic Reaction ? What is Eutectic Reaction? Which one is Eutectoid Reaction ? What is Eutectoid Reaction? How to identify the Reaction ?
  • 60.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 60 Which one is Eutectic Reaction ? What is Eutectic Reaction? Which one is Eutectoid Reaction ? What is Eutectoid Reaction? Which one is Peritectic Reaction ? What is Peritectic Reaction? How to identify the Reaction ?
  • 61.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 61 Which one is Eutectic Reaction ? What is Eutectic Reaction? Which one is Eutectoid Reaction ? What is Eutectoid Reaction? Which one is Peritectic Reaction ? What is Peritectic Reaction? How to identify the Reaction ?
  • 62.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 62 Which one is Eutectic Reaction ? What is Eutectic Reaction? Which one is Eutectoid Reaction ? What is Eutectoid Reaction? Which one is Peritectic Reaction ? What is Peritectic Reaction? How to identify the Reaction ? Confused ?
  • 63.
    BASIC COMPARISION Prepared byVISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 63 EUTECTIC REACTION EUTECTOID REACTION PERITECTIC REACTION Liquid phase Type-1 solid phase Type-2 solid phase Type-1 solid phase Type-2 solid phase Type-3 solid phase Type-1 solid phase Liquid phase Type-2 solid phase Note : There is no specific meaning of type 1, 2 & 3. It is just randomly used to differentiate the solid phases.
  • 64.
    CONGRUENT PHASE TRANSFORMATION •Phasetransformations may be classified according to whether or not there is any change in composition for the phases involved. •Those for which there are no compositional alterations are said to be congruent transformations. •It means phase changes without any change in wt% composition. Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 64
  • 65.
    CONGRUENT PHASE TRANSFORMATION Preparedby VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 65 Type – 1 phase with composition X wt% metal A Y wt% metal B
  • 66.
    CONGRUENT PHASE TRANSFORMATION Preparedby VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 66 Type – 1 phase with composition X wt% metal A Y wt% metal B Congruent Phase Transformation
  • 67.
    CONGRUENT PHASE TRANSFORMATION Preparedby VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 67 Type – 1 phase with composition X wt% metal A Y wt% metal B Type – 2 phase with same composition X wt% metal A Y wt% metal B Congruent Phase Transformation
  • 68.
    CONGRUENT PHASE TRANSFORMATION Prepared byVISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 68 A portion of the nickel–titanium phase diagram on which is shown a congruent melting point for the γ - phase solid solution at 1310OC and 44.9 wt% Ti.
  • 69.
    CONGRUENT PHASE TRANSFORMATION Prepared byVISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 69 A portion of the nickel–titanium phase diagram on which is shown a congruent melting point for the γ - phase solid solution at 1310OC and 44.9 wt% Ti.
  • 70.
    CONGRUENT PHASE TRANSFORMATION Prepared byVISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 70 A portion of the nickel–titanium phase diagram on which is shown a congruent melting point for the γ - phase solid solution at 1310OC and 44.9 wt% Ti. Congruent Phase Transformation L γ
  • 71.
    THE GIBBS PHASERULE Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 71 Josiah Willard Gibbs the nineteenth-century physicist
  • 72.
    THE GIBBS PHASERULE Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 72 Josiah Willard Gibbs the nineteenth-century physicist
  • 73.
    THE GIBBS PHASERULE P + F = C + N P = number of phases present F = number of degrees of freedom or the number of externally controlled variables (e.g., temperature, pressure, composition) C = number of components in the system N = number of noncompositional variables (e.g., temperature and pressure) • This rule represents a criterion for the number of phases that will coexist within a system at equilibrium Prepared by VISHAL MEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 73 Josiah Willard Gibbs the nineteenth-century physicist
  • 74.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 74 THE GIBBS PHASE RULE Continue…
  • 75.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 75 THE GIBBS PHASE RULE Continue… Consider that we want to find the number of degrees of freedom or the number of externally controlled variables for the single phase field of Cu-Ag system
  • 76.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 76 THE GIBBS PHASE RULE Continue… • Now Gibbs phase rule is P + F = C + N • Here • P = number of phases present • As we have considered single phase field, P = 1 • F = ? • C = number of components in system • As it is binary system, C = 2 • N = number of noncompositional variables (e.g., temperature and pressure) • Here we need to check that temperature & pressure are variable or not. • If both are variable, N = 2. If any one of two is variable, N = 1.
  • 77.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 77 THE GIBBS PHASE RULE Continue… • It has been discussed in initial phase of this chapter that for binary system Temperature and composition are variable parameters, and pressure is held constant—normally 1 atm. (slide no 17 & 24 of Part-1) • So here only temperature is variable, N = 1. • Gibbs phase rule is P + F = C + N • So 1 + F = 2 + 1 • F = 2
  • 78.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 78 THE GIBBS PHASE RULE Continue… • What is the meaning of F = 2 ? • This means that to completely describe the characteristics of any alloy that exists within one of these phase fields, we must specify two parameters; these are composition and temperature, which locate, respectively, the horizontal and vertical positions of the alloy on the phase diagram.
  • 79.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 79 meaning of F = 2 • In other words, it can be said that one can vary two parameters. • It means for any value of T, you may get more than one values of C & vice versa.
  • 80.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 80 THE GIBBS PHASE RULE Continue… • Now for the same example & same system, consider two phase field (instead of single phase). • So, P = 2 • Gibbs phase rule is P + F = C + N • So 2 + F = 2 + 1 • F = 1
  • 81.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 81 THE GIBBS PHASE RULE Continue… • What is the meaning of F = 1 ? • F = 1 means it is necessary to specify either temperature or the composition of one of the phases to completely define the system.
  • 82.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 82 meaning of F = 1 • Number of variable parameter is 1 • So, if you know any one value of three, remaining two values you can find. • For example if you know T1, you will get other two values of C & Cβ. • Or if you know C , you can find other two values.
  • 83.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 83 meaning of F = 1 • In other words, it can be said that one can vary only one parameter and other two will be changed. • It means for any value of T1, you will get one specific value of C & one specific value of Cβ. • (point can be any where on tie line/isotherm)
  • 84.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 84 THE GIBBS PHASE RULE Continue… • Now for the same example & same system, consider three phase field (instead of two phase). • So, P = 3 • Gibbs phase rule is P + F = C + N • So 3 + F = 2 + 1 • F = 0
  • 85.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 85 THE GIBBS PHASE RULE Continue… • What is the meaning of F = 0 ? • This means that the compositions of all three phases as well as the temperature are fixed.
  • 86.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 86 meaning of F = 0 • Number of variable parameter is 0. • It means values of T, CL, C & Cβ are fixed.
  • 87.
    Prepared by VISHALMEHTA || Reference : Material Science and Engineering, An Introduction by William D. Callister, Jr 87 END OF PART – 2 …. PLEASE CHECK PART – 3 ….