equilibrium diagrams having intermediate phases or compounds the magnesium–lead phase diagram....

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EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys, A. A. Nayeb-Hashemi and J. B. Clark (Editors), 1988 Reprinted by permission of ASM International, Materials Park, OH.] PHYSICAL METALLURGY (1) - 2012 R.EQRA

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Page 1: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS

The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys, A. A. Nayeb-Hashemi and J. B. Clark (Editors), 1988 Reprinted by permission of ASM International, Materials Park, OH.]

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 2: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PERITECTIC REACTIONS

Liquid + Solid1 Solid2

cooling

Heating

Therefore,this is an example of an incongruent-melting intermediate alloy

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 3: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 4: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Alloy 1, 90A-10B, remains liquid until the liquidus line is reached at T1. Solidification now takes place by forming crystals of the pure metal A. As the temperature falls, the liquid is decreasing in amount, and its composition is moving down along the liquid us line. Let us examine the conditions that exist just above the peritectic temperature Tp

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 5: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

The liquid contains 60A, while AmBn contains 70A. The liquid is not rich enough in A to form the compound by itself. The liquid must therefore react with just the right amount of solid A, in this case 8 percent, to bring its composition to that of the compound AmBn. The following reaction must have taken place at the peritectic temperature

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 6: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

The reaction takes place all around the surface of each grain of solid A where the liquid touches it. When the correct composition is reached,the layer solidifies into AmBn material surrounding every grain of A. Further reaction is slow since it must wait for the diffusion of atoms through the peritectic wall of AmBn in order to continue (see Fig. 6·40). When diffusion is completed, all the liquid will have been consumed, and since only 8 percent of pure A was required for the reaction, there will be 67 percent of A left. The final microstructure will show grains of primary A surrounded by the compound AmBn

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 7: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 8: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Since there was 87.5 percent liquid before the reaction and 50 percent liquid after the reaction, it is apparent that 37.5 percent of the liquid reacted with 12.5 percent of solid A to give 50 percent of the compound AmBn at the peritectic temperature

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 9: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

As cooling continues, the liquid now separates crystals of AmBn. The liquid becomes richer in B, and its composition gradually moves down and to the right along the liquidus line until it reaches point E, the eutectic temperature. At this temperature, there is only 5/50 x 100 or 10 percent liquid left. Since the liquid has reached the eutectic point, it now solidifies into the eutectic mixture of AmBn + B. This alloy, at room temperature, will consist of 90 percent primary or proeutectic AmBn surrounded by 10 percent of the eutectic (AmBn + B) mixture. Figure 6-42 shows the cooling curve and the changes in microstructure at various points in the slow cooling of this alloy.

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 10: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

β

αpt

Ag

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 11: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Monotectic reaction

Two liquids partly soluble in the liquid statePHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 12: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Two metal insoluble in the liquid and solid statesPHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 13: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Transformation in the solid state

Allotropy

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 14: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 15: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Order – disorder transformation

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 16: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 17: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 18: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

The eutectoid reactionPHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 19: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

ϒ

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 20: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

The peritectoid reactionPHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 21: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 22: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

ExamplesPHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 23: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 24: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Eutectoid reaction Peritectic reaction

A region of thecopper–zinc phase diagram thathas been enlarged to showeutectoid and peritecticinvariant points, labeled E

(560C, 74 wt% Zn )and P(598C, 78.6 wt% Zn,)

respectively. [Adapted fromBinary Alloy Phase Diagrams,2nd edition, Vol. 2, T. B.Massalski (Editor-in-Chief),

1990 .Reprinted by permissionof ASM International, Materials

Park, OH].

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 25: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

A portion ofthe nickel–titanium phasediagram on which isshown a congruent

melting point for the- phase solid solution at1310C and 44.9 wt% Ti.

[Adapted from PhaseDiagrams of Binary NickelAlloys, P. Nash (Editor),

1991 .Reprinted bypermission of ASMInternational, Materials

Park, OH].

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 26: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Figure 11-5A hypothetical phase diagram

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 27: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Considerations for effective dispersion strengthening: (a) The precipitate phase should be hard and discontinuous, while the matrix should be continuous and soft, (b) the dispersed phase particles should be small and numerous, (c) the dispersed phase particles should be round rather than needle-like, and (d) larger amounts of the dispersed phase increase strengthening.

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 28: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Phase Rule

Josiah Willard Gibbs (1839–1903) was a brilliant American physicist and mathematician who conducted some of the most important pioneering work related to thermodynamic equilibrium

Gibbs developed the phase rule in 1875–1876. It describes the relationship between the number of components and the number of phases for a given system and the conditions that may be allowed to change (e.g., temperature , pressure, etc.). It has the general form:

C is the number of chemically independent components, usually elements or compounds, in the system; F is the number of degrees of freedom, or the number of variables (such as temperature, pressure, or composition), that are allowed to change independently without changing the number of phases in equilibrium; and P is the number of phases present (please do not confuse P with “pressure”).

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 29: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

at point A

at point B

at point X

Unary systemPHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 30: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Binary systemPHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 31: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 32: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Eutectic , peritectic , eutectoid , peritectoid , monotectic

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 33: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Ternary phase diagramPHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 34: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 35: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYS

ICAL

MET

ALLU

RGY

(1) -

201

2 R.

EQRA

Page 36: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Example

PHYSICAL METALLURGY (1) - 2012 R.EQRA

Page 37: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

PHYS

ICAL

MET

ALLU

RGY

(1) -

201

2 R.

EQRA

Page 38: EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS The magnesium–lead phase diagram. [Adapted from Phase Diagrams of Binary Magnesium Alloys,

Freeze near 360oC, with primary β forming first. Near 275oC, ϒ will also begin to form. Finally, at 160oC,α forms and the last liquid freezes. The final microstructure contains α , β , and ϒ.

PHYS

ICAL

MET

ALLU

RGY

(1) -

201

2 R.

EQRA