1. Phases and the Phase Diagram
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Phases and the Phase Diagram
Pure metallic elements have engineering applications; for example, ultra-high purity copper (Cu) or aluminum (Al) is used to make microelectronic circuitry. In most applications, however, we use alloys. We define an “alloy” as a material that exhibits properties of a metallic material and is made from multiple elements. A plain carbon steel is an alloy of iron (Fe) and carbon (C). Corrosion resistant stainless steels are alloys that usually contain iron (Fe), carbon (C), chromium (Cr), nickel (Ni), and some other elements. Similarly, there are alloys based on aluminum (Al), copper (Cu), cobalt (Co), nickel (Ni), titanium (Ti), zinc (Zn), and zirconium (Zr). There are two types of alloys: single-phase alloys and multiple phase alloys.

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The understanding of phase diagrams for alloy systems is extremely important because there is a strong correlation between microstructure and mechanical properties, and the development of microstructure of an alloy is related to the characteristics of its phase diagram. In addition, phase diagrams provide valuable information about melting, casting, crystallization, and other phenomena
unary phase diagram
one-component phase diagram (or unary phase diagram) [sometimes also called a pressure–temperature (or P–T) diagram] is represented as a two dimensional plot of pressure (vertical axis) versus temperature ( horizontal axis)

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Pressure–temperature phase diagram for H2O. Intersection of the dashed horizontal line at 1 atm pressure with the solid–liquid phase boundary (point 2) corresponds to the melting point at this pressure (T 0C). Similarly, point 3, the intersection with the liquid–vapor boundary, represents the boiling point (T 100C).

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Schematic unary phase diagram for magnesium, showing the melting and boiling temperatures at one atmosphere pressure. On this diagram, point X is the triple point

5. BINARY ISOMORPHOUS SYSTEMS
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BINARY ISOMORPHOUS SYSTEMS

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(a) The copper–nickel phase diagram. (b) A portion of the copper nickel phase diagram for which compositions and phase amounts are determined at point B. (Adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash, Editor, Reprinted by permission of ASM International, Materials Park, OH.)

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Figure 10-12

9. Lever Rule Derivation (mass balance)
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Lever Rule Derivation
(mass balance)

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Equilibrium Cooling

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

14. Nonequilibrium Cooling
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Nonequilibrium Cooling

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16. Schematic representation of the development of microstructure
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Schematic
representation of the
development of
microstructure
during the
nonequilibrium
solidification of a 35
wt% Ni–65 wt% Cu
alloy.

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Figure The change in structure of a Cu 40% Ni alloy during nonequilibrium solidification. Insufficient time for diffusion in the solid produces a segregated structure. Notice the nonequilibrium solidus curve

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To summarize
Nonequilibrium cooling results in an increased temperature range over which liquid and solid are present;
Final solidification occurs at a lower temperature than predicted by the phase diagram;
The final liquid to solidify will be richer in the lower-meltinq-point metal; and since diffusion has not kept pace with crystal growth. There will be a difference in chemical composition from the center to the outside of the grains.
The faster the rate of cooling. the greater will be the above effects

19. Homogenization Cored structures are most common in as-cast metals
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Homogenization
Cored structures are most common in as-cast metals
From the discussion of the origin of a cored structure. it is apparent that the last solid formed along the grain boundaries and in the interden dritic spaces is very rich in the lower-melting-point metal. Depending upon the properties of this lower-melting-point metal, the grain boundaries may act as a plane of weakness. It will also result in a serious lack of uniformity in mechanical and physical properties and, in some cases, increased susceptibility to intergranular corrosion because of preferential attack by a corrosive medium. Therefore, for some applications, a cored structure is objectionable

20. Diffusion There are two methods for solving the problem of coring
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There are two methods for solving the problem of coring
One is to prevent its formation by slow freezing from the liquid, but this results in large grain size and requires a very long time.
The preferred method industrially is to achieve equalization of composition or homogenization of the cored structure by diffusion in the solid state
Diffusion
Diffusion refers to the net flux of any species, such as ions, atoms, electrons, holes and molecules. The magnitude of this flux depends upon the concentration gradient and temperature.

21. Rate of Diffusion [Fick’s First Law]
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Rate of Diffusion [Fick’s First Law]
The rate at which atoms, ions, particles or other species diffuse in a material can be measured by the flux J
The flux J is defined as the number of atoms passing through a plane of unit area per unit time.
Fick’s first law explains the net flux of atoms:

22. Temperature and the Diffusion Coefficient
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Temperature and the Diffusion Coefficient
The kinetics of diffusion are strongly dependent on temperature. The diffusion coefficient D is related
Composition Profile [Fick’s Second Law]
Fick’s second law, which describes the dynamic, or non-steady state, diffusion of atoms, is the differential equation
For example

23. Mechanisms for Diffusion
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Mechanisms for Diffusion

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27. MECHANICAL PROPERTIES OF ISOMORPHOUS ALLOYS
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MECHANICAL PROPERTIES OF ISOMORPHOUS ALLOYS
For the copper–nickel system, (a) tensile strength versus composition, and (b) ductility (%EL) versus composition at room temperature. A solid solution exists over all compositions for this system.

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29. CONGRUENT PHASE TRANSFORMATIONS
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CONGRUENT PHASE TRANSFORMATIONS

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(a) Using this diagram, briefly explain how spreading salt on ice that is at a temperature below 0°C (32°F) can cause the ice to melt.
(b) At what temperature is salt no longer useful in causing ice to melt?

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33. BINARY EUTECTIC SYSTEMS
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BINARY EUTECTIC SYSTEMS
The copper–silver phase diagram. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.]

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The lead–tin phase diagram. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.

35. DEVELOPMENT OF MICROSTRUCTURE IN EUTECTIC ALLOYS
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DEVELOPMENT OF MICROSTRUCTURE IN EUTECTIC ALLOYS
Schematic representations of the equilibrium microstructures for a lead–tin alloy of composition C1 as it is cooled from the
liquid-phase region

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37. representations of the equilibrium microstructures
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Schematic
representations of the
equilibrium microstructures
for a lead–tin alloy of
composition C2 as it is
cooled from the liquidphase
region.

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Schematic representations of the equilibrium microstructures for a lead–tin alloy of eutectic composition C3 above and below the eutectic temperature

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Schematic representations of the equilibrium microstructures for a lead–tin alloy of composition C4 as it is cooled from the liquid-phase region

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47. Age or Precipitation Hardening
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Age or Precipitation Hardening
Age hardening, or precipitation hardening, is produced by a sequence of phase transformations that leads to a uniform dispersion of nanoscale, coherent precipitates in a softer, more ductile matrix
Step 1: Solution Treatment
In the solution treatment, the alloy is first heated above the solvus temperature and held until a homogeneous solid solution α is produced
Step 2: Quench
After solution treatment, the alloy, which contains only α in its structure, is rapidly cooled, or quenched. The atoms do not have time to diffuse to potential nucleation sites, so the θ does not form
supersaturated solid solution αss containing excess copper, and it is not an equilibrium structure. It is a metastable structure

48. Step 3: Age
Finally, the supersaturated is heated at a temperature below the solvus temperature. At this aging temperature, atoms diffuse only short distances. Because the supersaturated is metastable, the extra copper atoms diffuse to numerous nucleation sites and precipitates grow. Eventually, if we hold the alloy for a sufficient time at the aging temperature, the equilibrium structure α+θ is produced
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50. Coherent Precipitate
Even if we produce a uniform distribution of discontinuous precipitate, the precipitate may not significantly disrupt the surrounding matrix structure (noncoherent)[Figure (a)]. Consequently, the precipitate blocks slip only if it lies directly in the path of the dislocation.
When a coherent precipitate forms, the planes of atoms in the crystal structure of the precipitate are related to—or even continuous with—the planes in the crystal structure of the matrix [Figure (b)]. Now a widespread disruption of the matrix crystal structure is created, and the movement of a dislocation is impeded even if the dislocation merely passes near the coherent precipitate. A special heat treatment, such as age hardening, may produce the coherent precipitate.
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53. Nonequilibrium Precipitates during Aging
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Nonequilibrium Precipitates during Aging
During aging of aluminum-copper alloys, a continuous series of other precursor precipitate phases forms prior to the formation of the equilibrium phase. At the start of aging, the copper atoms concentrate on {100} planes in the matrix and produce very thin precipitates called Guinier-Preston (GP) zones. As aging continues, more copper atoms diffuse to the precipitate and the GP-I zones thicken into thin disks, or GP-II zones. With continued diffusion, the precipitates develop a greater degree of order and are called θ’. Finally, the stable θ precipitate is produced. The nonequilibrium precipitates—GP-I, GP-II, and θ’ are coherent precipitates. The strength of the alloy increases with aging time as these coherent phases grow in size during the initial stages of the heat treatment. When these coherent precipitates are present, the alloy is in the aged condition. When the stable noncoherent θ phase precipitates, the strength of the alloy begins to decrease. Now the alloy is in the overaged condition. The still provides some dispersion strengthening, but with increasing time, the grows larger and even the simple dispersion-strengthening effect diminishes.

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Aging at either 190°C or 260°C is called artificial aging because the alloy is heated to produce precipitation. Some solution treated and quenched alloys age at room temperature; this is called natural aging

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