1. EQUILIBRIUM DIAGRAMS HAVING INTERMEDIATE PHASES OR COMPOUNDS
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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.]

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PERITECTIC REACTIONS
cooling
Liquid + Solid Solid2
Heating
Therefore,this is an example of an incongruent-melting intermediate alloy

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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

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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

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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

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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

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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 shows the cooling curve and the changes in microstructure at various points in the slow cooling of this alloy.

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11. Two liquids partly soluble in the liquid state
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Two liquids partly soluble in the liquid state
Monotectic reaction

12. Two metal insoluble in the liquid and solid states
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Two metal insoluble in the liquid and solid states

13. Transformation in the solid state
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Transformation in the solid state
Allotropy

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15. Order – disorder transformation
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Order – disorder transformation

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18. The eutectoid reaction
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The eutectoid reaction

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20. The peritectoid reaction
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The peritectoid reaction

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Examples

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24. Eutectoid reaction Peritectic reaction A region of the
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A region of the
copper–zinc phase diagram that
has been enlarged to show
eutectoid and peritectic
invariant points, labeled E
(560C, 74 wt% Zn) and P
(598C, 78.6 wt% Zn),
respectively. [Adapted from
Binary Alloy Phase Diagrams,
2nd edition, Vol. 2, T. B.
Massalski (Editor-in-Chief),
1990. Reprinted by permission
of ASM International, Materials
Park, OH.]
Eutectoid reaction
Peritectic reaction

25. the nickel–titanium phase diagram on which is shown a congruent
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A portion of
the nickel–titanium phase
diagram on which is
shown a congruent
melting point for the -
phase solid solution at
1310C and 44.9 wt% Ti.
[Adapted from Phase
Diagrams of Binary Nickel
Alloys, P. Nash (Editor),
1991. Reprinted by
permission of ASM
International, Materials
Park, OH.]

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Figure 11-5
A hypothetical phase diagram

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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.

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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”).

29. Unary system at point A at point B at point X
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Unary system
at point A
at point B
at point X

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Binary system

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32. Eutectic , peritectic , eutectoid , peritectoid , monotectic
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Eutectic , peritectic , eutectoid , peritectoid , monotectic

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Ternary phase diagram

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36. Example
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38. Freeze near 360oC, with primary β forming first
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.
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