CHAPTER 8. Phase Diagrams 8-1

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CHAPTER

8

Phase

Diagrams

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Introducción

• Fase: Una region en un material que difiere en estructura y función de otra región.

• Diagramas de fase :

Representan las fases presentes en el metal a diferentes

condiciones (Temperatura, presión y composición).

Indica la solubilidad de un sólido en equilibrio en otro elemento.

elemento.

Indica el rango de temperatura en el cual ocurre la solidificación.

Indica la temperatura a la cual las diferentes fases inician

su fusión.

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Diagram de fase de substancias puras

• Las sustancias puras existen en estado sólido,

líquido y vapor.

• Las fases estan separadas por límites de fase

Ejemplo : Agua, Hierro puro.

• Diferentes fases coexisten en el

punto triple.

Figure 8.1 Figure 8.2

After W. G. Moffatt, et al., “The Structure and Properties of Materials,” vol I: “Structure,” Wiley, 1965, p.151 8-3

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REGLA DE LAS FASES DE GIBBS

• P+F = C+2

• Para el agua pura, en el punto triple, coexisten 3 fases.

• Hay un componente (agua) en el sistema.

• Así que 3 + F = 1 + 2 F = 0.

P = número de fase que coexisten en un sistema C = Numero de componentes

F = Grados de libertad

• Así que 3 + F = 1 + 2 F = 0.

• Los grados de libertad indican el número de variable que pueden ser cambiadas sin que cambie el número de fases.

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Curvas de enfriamiento en equilibrio

• Usedas para determinar la temperatura de

transición de la

fase

.

Pure Metal

• Meseta térmica :

pérdida de calor = calor necesario

para solidifacar el metal.

• Las aleaciones solidifican en un

rango de

temperatura

(sin meseta térmica)

Pure Metal

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Sistema de aleación Binario Isomorfo

Aleación binaria

• Sistema Isomorfo : Los dos elementos son completamente

solubles en estado líquido y en estado sólido. Ejemplo: Cu-Ni solución.

Sistema de dos componentes

La Composición de las fases puede ser determinada A cualquier temperatura

en forma gráfica.

Figure 8.3

Adapted from “Metals Handbook,” vol. 8, 8th_{ed., American society of Metals, 1973, p. 294.}

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Phase Diagram from Cooling Curves

• Series of cooling curves at different metal composition are first constructed.

• Points of change of slope of cooling curves (thermal arrests) are noted and phase diagram is constructed.

• More the number of cooling curves, more accurate is the phase diagram.

the phase diagram.

Figure 8.4

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The Lever Rule

• The Lever rule gives the weight % of phases in any two phase regions.

Wt fraction of solid phase = X_s = w₀ – w₁

w – w w_s – w₁

Wt fraction of liquid phase = X1 = ws – w0

ws – w1

Figure 8.5

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Non Equilibrium Solidification of Alloys

• Very slow cooling (equilibrium) gives rise to cored structure.

• Rapid cooling delays solidification.

• Homogenization: Cast ingots heated to elevated temperature to eliminate

cored structure.

• Temperature of homogenization

• Temperature of homogenization must be lower than lowest melting point of any of the alloy components.

Figure 8.7 Figure 8.8

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Binary Eutectic Alloy System

• In some binary alloy systems, components have limited solid solubility.

• Eutectic composition freezes

at lower temperature than all other compositions.

Example : Pb-Sn alloy.

• This lowest temperature is

called eutectic temperature.

Liquid α solid solution + β solid solution

Eutectic temperature Cooling

Figure 8.11

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Slow Cooling of 60% Pb – 40% Sn alloy

• Liquid at 3000C.

• At about 2450C first

solid forms – proeutectic solid.

• Slightly above 1830C composition of alpha

Figure 8.12

composition of alpha follows solidus and

composition of sn varies from 40% to 61.9%.

• At eutectic temperature, all the remaining liquid solidifies.

• Further cooling lowers alpha Sn content and beta Pb.

Figure 8.13

From J. Nutting and R. G. Baker, “Microstructure of Metals,” Institute of Metals, London, 1965,p.19. 8-10

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Various Eutectic Structures

• Structure depends on factors like minimization of free

energy at α / β interface.

• Manner in which two phases nucleate and grow also affects structures.

Figure 8.14

After W. C. Winegard, “An Introduction to the Solidification of Metals,” Institute of Metals, London, 1964. 8-11

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Binary Peritectic Alloy System

• Peritectic reaction: Liquid phase reacts with a solid

phase to form a new and different solid phase. Liquid + α β

cooling

• Peritectic reaction occurs

when a slowly cooled alloy of Fe-4.3 wt% Ni passes of Fe-4.3 wt% Ni passes

through Peritectic

temperature of 15170C.

• Peritectic point is invariant.

Liquid(5.4 wt% Ni) + δ (4.0 wt% Ni) γ 4.3 wt % Nicooling

Figure 8.16

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Peritectic Alloy System

• At 42.4 % Ag & 14000_C

Phases present Liquid Alpha

Composition 55% Ag 7%Ag Amount of Phases 42.4 –7 55-42.4

55 – 7 55 - 7 = 74% = 26%

• At 42.4% Ag and 11860_{C – ∆T}

Phase Present Beta only Phase Present Beta only Composition 42.4% Ag Amount of Phase 100%

• At 42.4% Ag and 11860_{C + ∆T}

Phases present Liquid Alpha

Composition 66.3% Ag 10.5%Ag Amount of Phases 42.4 –10.5 66.3-42.4 66.3 – 10.5 66.3–10.5 = 57% =43% Figure 8.17 Figure 8.18 8-13

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Rapid Solidification in Peritectic System

• Surrounding or Encasement: During peritectic

reaction, L+ α β , the beta phase created surrounds primary alpha.

• Beta creates diffusion barrier resulting in coring.

Figure 8.20

Figure 8.19

After F Rhines, “ Phase Diagrams in Metallurgy,”McGraw- Hill, 1956, p. 86. 8-14

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Binary Monotectic Systems

• Monotectic Reaction: Liquid phase transforms into

solid phase and another liquid. L₁ Cooling α + L₂

• Two liquids are immiscible. • Example:- Copper – Lead

system at 9550C and 36% Pb. Eutectic Eutectoid Peritectic Peritectoid Monotectic Figure 8.23 Table 8.1

Metals Handbook,” vol. 8: “Metallography Structures and Phase Diagrams,” 8th_{ed., American Society of Metals, 1973, p. 296.}

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Intermediate Phases and Compounds

• Terminal phases:

Phases occur at the end of phase diagrams.

• Intermediate phases:

Phases occur in a

composition range inside phase diagram.

phase diagram.

• Examples: Cu-Zn diagram has both terminal and

intermediate phases.

• Five invariant peritectic points and one eutectic point.

Figure 8.25

“Metals Handbook,” vol. 8: “Metallography Structures and Phase Diagrams,” 8th_{ed., American Society of Metals, 1973, p. 301}

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Intermediate Phases in Ceramics

• In Al₂O₂ – SiO₂ system, an intermediate phase called

Mullite is formed, which includes the compound

3Al₂O₃.2SiO₂.

Figure 8.26

After A. G. Guy, “Essentials of Materials Science, “McGraw-Hill, 1976 8-17

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Intermediate Compounds

• In some phase diagrams, intermediate compound are formed – Stoichiometric

• Percent Ionic/Covalent bond depends on electronegativeness

• Example:- Mg-Ni phase diagram contains

Mg2Ni : Congruently melting compound MgNi2 : Incongruently melting compound. MgNi2 : Incongruently melting compound.

Figure 8.27

Metals Handbook,” vol. 8: American Society of Metals, 1973, p. 314. 8-18

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Ternary Phase Diagrams

• Three components

• Constructed by using a equilateral triangle as base.

• Pure components at each

end of triangle.

• Binary alloy composition

represented on edges. represented on edges.

Temperature can be represented as uniform throughout the Whole Diagram Isothermal section.

Figure 8.28

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Ternary Phase Diagram (Cont..)

• Example:- Iron-Chromium-Nickel phase diagrams.

•Isothermal reaction at 6500C

for this system

• Composition of any metal

at any point on the phase at any point on the phase diagram can be found by

drawing perpendicular

from pure metal corner to apposite side and calculating

the % length of line at that

point

Figure 8.30

After “Metals Handbook,” vol. 8: American Society of Metals, 1973, p. 425. 8-20