1. CHAPTER 8
Phase Diagrams
and
Microstructure
Development

2. 8-II. DEFINITIONS AND BASIC CONCEPTS
8-I. Introduction
There is a strong correlation between microstructure and mechanical properties, microstructure is related to phase diagram.
Phase diagarms provide valuable information about melting, casting, crystallization, and other phenomena.
8-II. DEFINITIONS AND BASIC CONCEPTS
Component：pure metals and/or compounds e.g., copper-zinc brass, the components are Cu and Zn.
System：A specific body of material under consideration or series of possible alloys consisting of the same components.

3. Solute : atoms occupy either substitutional or interstitial positions in the solvent lattice, and the crystal structure of the solvent is maintained.
A. SOLUBILITY LIMIT
Maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution; Solubility limit depends on the temperature
F9.1

4. B. PHASES
Phase:
A homogeneous portion of a system that has uniform physical and chemical characteristics. Every pure material is considered to be a phase.
A single-phase system is termed “homogeneous” or “ a homogeneous system.”
Systems composed of two or more phases are termed “mixtures” or “heterogeneous systems.”
Most metallic alloys, ceramic, polymeric, and composite are heterogenous materials .
F10-11
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5. C. MICROSTRUCTURE
Microstructure is subject to direct microscopic observation, using optical or electron microscopes
In metal alloys, microstructure: number of phases present, their proportions and the manner they are distributed or arranged.
Microstructure depends:
Elements present, their concentrations, heat treatment (i.e., the temperature, the heating time at temperature, and the rate of cooling to room temperature).
Specimen preparation (polishing and etching):
different phases may be distinguished by their appearance, light or dark,

6. D. PHASE EQUILIBRIA Equilibrium
Free energy: A function of the Internal energy of a system, and also the randomness or disorder of the atoms or molecules (or entropy).
A system is at equilibrium if its free energy Gibbs energy, G is at a minimun
The characteristics of the system do not change with time but persist indefinitely; that is, the system is stable.
Phase equilibrium
A constancy with time in the phase characteristics, e-g., Sugar-water syrup at 20°C.

7. In materials systems,characteristics of the microstructure:
65wt% C12H22O11–35wt% H2O
at 100°C : 80wt% C12H22O11
F9.1
In materials systems,characteristics of the microstructure:
the phases present
their compositons
relative phase Amounts
their spatial arrangement or distribution.
Free energy considerations and diagrams
F9-2
Phase diagrams are made with the assumption that the systems are at equilibrium.
In practical situations, systems are often not at equilibrium.

8. Phase diagrams do not indicate the time period necessary for the attainment of a new equilibrium state. It is often that a state of equilibrium is never completely achieved because the rate of approaching is slow.
Nonequilibrium or metastable state.
Often, metastable structures are of more practical sighinficance than equilibrium ones.
The speed or rate at which they are established and the factors that affect the rate must be considered.

9. E. EQUILIBRIUM PHASE DIAGRAMS
F10-12
Phase diagram (equilibrium or constitutional diagram.) : Relationships between temperature and the compositions and the quantities of phases at equilibrium.
at least three kinds of information are available (1) the phase that are present, (2) the compositions of these phases, and (3) the percentages or fractions of the phases
Pressure is also a parameter that influences the phase structure. However, pressure remains constant in most applications
Ordinary phase diagrams (and the ones presented here) are for a constant pressure of one atmosphere (1 atm).
Ordinate: temperture; abscissa: composition (weight percent and atom percent )
F9-2

10. 8-III. Phase Diagram of Metallic Materials
Isomorphous System (phase Diagram)
Eutectic System (phase Diagram)
Phase Diagram with Intermediate phases or compounds

11. 8-III-1 BINARY ISOMORPHOUS SYSTEMS F9.2a
Binary: a system that contains two components.
Isomorphous：the components can be dissolved into each other completely without solubility limits.
F9-3a
For example: Figure 9.2
(a) Three different phase regions, or fields:
An alpha ( ) field, a liquid (L) field, a two-phase +L field
Liquid L : a homogeneous liquid solution composed of both copper and nickel

12. α Phase : a substitutional solid solution consisting of both Cu and Ni atoms and having an FCC crvstal structure α , complete solublity : both Cu and Ni have the same crystal structure (FCC) , nearly identical atomic radij and electronegativities, similar valences ⇒ Isomorphous
Solid solutions: desinated by lowercase Greek letters (   etc.).
Two-phase region
Liquidus line
Solidus line

13. (b) Melting temperatures
F9.3a
Pure component
solid-to-liquid transformation takes place at the melting temperature, and no further heating increase in temperature is possible until this transformation has been completed
Solid solution
for any composition of solid solution, melting phenomenon will occur over the range of temperatures between the solidus and liquidus lines, both solid  and liquid phases will be in equilibrium within this temperature range
F9.3b

14. A. INTERPRETATION OF PHASE DIAGBAMS
at least three kinds of information are available (1) the phase that are present, (2) the compositions of these phases, and (3) the percentages or fractions of the phases
F9-3b
PHASES PRESENT F9.3a
For example : Figure 9.3
60wt% Ni-40wt% Cu at 1100C : point A , single  phase
35wt% Ni-65wt% Cu alloy at 1250C : point B ,  and liquid phases at equilibrium.

15. DETERMINATION OF PHASE COMPOSITIONS
(a) one phase region : same as the overall composition
e.g., point A ,α phase having a composition of 60wt% Ni-40wt% Cu
(b) two-phase region
F9.3a
tie line : horizontal lines (isotherm) across the two-phase region and terminate at the phase boundary lines
tie line-liquidus intersection : 31.5wt% Ni-68.5wt% Cu composition of the liquid phase CL :
solidus-tie line ntersection :C , 42.5wt% Ni-57.5wt% Cu
F9.3b

16. DETERMINATION OF PHASE AMOUNTS
(a) single-phase region：e.g., point A
only the  phase is present , 100% 
(b) two-phase region
The tie line must be utilized : lever rule (or the inverse lever rule)
The fraction of one phase is computed by taking the length of tie line from the overall alloy composition to the phase boundary for the other phase , and dividing by the total tie line length.
For example : point B in Figure 9.3b
35 wt% Ni-65 wt% Cu alloy
overall alloy composition：C0
mass fractions WL and W
F9.3b

17. (9.1a)
(9.1b)
(9.2a)
(9.2b)

18. B. Development of Microstructure in Isomorphous Alloys
Equilibrium Cooling: Cooling occurs very slowly, phase equilibrium is continuously maintained.
(microsfructure equilibrium cooling;
nonequilibrium noneqiilibrium cooling)
Process of Solidification
Nucleation: the formation of initial solid phase
(very beginning step of solidification)
(2) growth of the nuclei
(3) maturity of microstructure: grain, grain boundary (polycrystalline)
initial solid phase: in the form of small particles nuclei

19. The final product then is a polycrystalline -phase solid solution .
Example: copper-nickel system (Figure 9.3a), 35wt% Ni-65 wt% Cu is cooled from 1300℃.
at point b, ~1260℃, first solid  begins to form, 46wt% Ni-54wt% Cu, noted as (46Ni) .
The overall alloy composition (35wt% Ni-65wt% Cu) remains unchanged during cooling.
The solidification process is complete at about 1220℃, point d, last remaining liquid: 24wt% Ni-76wt% Cu.
The final product then is a polycrystalline -phase solid solution .
F9.4

20. Nonequilibrium cooling
Equilibrium solidification : readjustments in the compositions of the liquid and solid phases must occur (by diffusion)
Nonquilibrium solidification:
In virtually all practical solidification situations, cooling rates are much too rapid to allow compositional readjustments in the solid phases: nonequilibrium solidification (but assumed that diffusion rates in the liquid phase are sufficiently rapid such that equilibrium is maintained in the liquid).
Example：Fig.9.4
F9.5
F9.4

21. Point c’ (about 1240℃), liquid composition 29wt% Ni-71wt% Cu;  phase that solidified is 40wt% Ni-60wt% Cu [(40 Ni)]. The composition of the  grains has continuously changed with radial position, from 46wt% Ni at grain centers to 40wt% Ni at the outer grain perimeters. Average composition : 42wt% Ni-58wt% Cu [(42 Ni)].
The solidus line has been shifted to higher Ni contents-to the average compositions of the  phase. At point e’ (~1250℃) , the last  phase: 31wt% Ni , average 35wt% Ni.

22. The distribution of the two elements within the grains is nonuniform:
nonuniform composition: segregation (concentration gradients, the center of each grain, is rich in the high-melting element: cored sturcture).
Cored structure:
Grain boundary regions will melt first as they are richer in the low-melting component cored structure has a lower melting point. This produces a sudden loss in mechanical integrity.
Furthermore, this melting may begin at a temperature below the equilibrium solidus temperature of the alloy. Coring may be eliminated by a homogenization heat treatment at a temperature below the solidus point for the particular alloy composition.

23. Mechanical Properties Of Isomorphous Alloys
Solid-solution strengthening (Section 7.9): an increase in strength and hardness by additions of the other component.
F9-6
8-III-2. Binary Eutectic Systems
For example: the copper-silver system.
three single-phase regions , , and liquid.
 phase : a solid solution rich in copper, silver as the solute FCC crystal structure.
-phase：solid solution FCC structure, copper is the solute.
The  and  phases are considered to include pure copper and pure silver, respectively.
F9.7

24. The solubility limit for the  phase has a maximum [8
The solubility limit for the  phase has a maximum [8.0 wt% Ag] at 779°C (1434 °F ), point B.
Solubility limit line separating the  and + phase regions : solvus line. Boundary AB between the  and +L fields: solidus line.
Maximum solubility in the  Phase: point G .
Horizontal line BEG, a solidus line, the lowest temperature at which a liquid phase may exist.
Three two-phase regions:  + L,  + L and  + .

25. L(71.9 wt% Ag) (8.0 wt% Ag) + (91.2 wt% Ag)
The melting temperature of copper is lowered by silver additions. The same may be said for silver.
Point E is called an invariant point: the composition CE and temperature TE; (71.9 wt% Ag and 779℃) (9-8)
L(CE) (CE) + (CE)
cooling
heating
F 9.7
Eutectic reaction (eutectic means easily melted), CE and TE the eutectic composition and eutectic temperature, respetctively; (CE and CE)
L(71.9 wt% Ag) (8.0 wt% Ag) + (91.2 wt% Ag)
cooling
heating
The horizontal solidus line at TE : eutectic isotherm (eutectic phase diagrams , eutectic system)

26. A. Consturction of Binary Phase Diagrams
In general, one or at most two phases may be in equilibrium within a phase field.
for a eutectic system, three phases (, , and L) may be in equilibrium, but only at points along the eutectic isotherm.
single-phase regions are always separated from each other by a two-phase region.
B. Another common eutectic system: lead and tin
F9.8
Low-melting-temperature alloys : having near-eutectic compositions, example: solder, 60 wt% Sn and 40 wt% Pb.
F9.9
Rules

27. C. Development of Microstructure In Eutectic Alloys
(a) The first case : between a pure component and the maximum solid solubility at room temperature (0 – ~ 2wt% Sn)
F9.9
F9.11
(b) The second case : between the room temperature solubility limit and the maximum solid solubility at the eutectic temperature. (2wt% Sn–18.3wt% Sn)
F9.12
Upon crossing the solvus line, the  solid solubility is exceeded, which results in the formation of small -phase particles (nucleation) , these particles will grow in size because the mass fraction of the  phase increases with decreasing temperature.

28. (c) The third case : the eutectic composition.
Upon crossing the eutectic isotherm, the liquid transforms to the two  and  phases
F9.13
cooling
(9.9)
L(61.9 wt% Sn) (18.3 wt% Sn) + (97.8 wt% Sn)
heating
By atomic diffusion : alternating layers (lamellase )of the  and  phases (eutectic structure) , atomic diffusion of short distances
F9.14
F9.15
(d) The fourth case :
Eutectic α, primary α. microconstituent , two microconstituents : primary  and the eutectic structure.
Fraction of the eutectic microconstituent we and fraction of liquid wL
(9-10)
F9.16
F9.17
F9.18

29. fraction of primary , W’
(9.11)
Fraction of total , W (both eutectic and primary) , total , W
(9.12)
(9.13)

30. fraction of primary + fraction of eutectic
When, for case 4, conditions of equilibrium are not maintained :
grains of the primary microconstituent will be cored ,
the fraction of the eutectic microconstituent will be
greater than for the equilibrium situation.

31. 8-III-3. Equilibrium Diagrams Having Intermediate Phases or Compounds
Terminal solid solutions: the solid solutions at each end.
Intermediate solid solutions (or intermediate phases):
the solid solutions in between:
Comparison
F9.19
For example:
the copper-zinc system
There are six different solid solutions-two terminal ( and ) and four Intermediate (, , , and ∈). (the ’ phase: a specific and ordered arrangement). Dashed phase boundary lines : not determined.
The commercial brasses are copper-rich copper-zinc alloys.

32. For some systems: intermetallic compounds.
the magnesium-lead system compound, Mg2Pb (19wt% Mg-81wt% Pb): a vertical line.
For example,
(1) Mg2Pb melts at 550℃ (M) ,
(2) The solubility :
(3) This phase diagram may be thought of as two simple eutectic diagrams joined back to back: Mg-Mg2Pb system and Mg2Pb-Pb; Mg2Pb is really considered to be a component.

33. A. Eutectoid and Peritectic Reactions
Invariant points (involving three different phases):eutectoid
(9.14)
F9.21
F9.19
eutectoid (or eutectic-like) reaction
eutectoid isotherm
distinguishing “eutectoid” from “eutectic” : one solid phase instead of a liquid transforms into two other solid phases at a single temperature.
A eutectoid reaction is found in the iron-carbon system (section 9.17) that is very important in the heat treating of steels.

34. B. CONGRUENT PHASE TRANSFORMATIONS
Peritectic reaction (another invariant reaction):one solid phasetransforms into a liquid phase and another solid phase.
(9.15)
F9.19
B. CONGRUENT PHASE TRANSFORMATIONS
Phase transformations without compositional alterations: congruent transformations, e.g., melting of pure materials and intermetallic compounds; with a change in composition : incongruent tansformations ,e.g., eutectic and eutectoid reactions.

35. C. THE IRON-CARBON SYSTEM
Both steels and cast irons, are essentially iron-carbon alloys.
F9.24
THE IRON-IRON CARBIDE (Fe-Fe3C)PHASE DIAGRAM
(a)Pure iron, upon heating, experiences two changes in crystal structure before it melts. At room tempeature: ferrite, or αiron, has a BCC crystal structure; At 912 ° C, FCC austenite, or γ iron; at 1394 ° C, BCC phase, δferrite; finally melts at 1538 ° C (2800 ° F ).

36. Carbon is an interstitial impurity in iron.
The composition extends only to 6.70 wt% C, an intermediate compound: iron carbide, or cementite (Fe3C)
Carbon is an interstitial impurity in iron.
In the BCC α ferrite, only small concentrations of carbon are soluble; (explained by the shape and size of the BCC interstitial positions.)
Relatively soft, may be made magnetic.
The austenite, or γ phase of iron, solubility is approximately 100 times greater than for BCC ferrite since the FCC interstitial positions are larger. Austenite is nonmagnetic.
Mechanically, cementite is very hard and brittle; the strength of some steels is greatly enhanced by its presence.
F9.24

37. (b). DEVELOPMENT OF MICROSTRUCTURE IN IRON-CARBON ALLOYS
From the γ region into the α + Fe3C phase field with eutectoid composition (0.76wt% C): lamellae, relative layer thickness ( α to Fe3C): 8 to 1: pearlite ( because it has the appearance of mother of pearl), with grains termed “colonies”.
Pearlite has properties intermediate between the soft, ductile ferriteand the hard, brittle cementite.
The alternating α and Fe3C layers in pearlite form by carbon diffusion from the wt% ferrite regions and to the 6.7 wt% cementite layers.
F9.26
F9.27
F9.28

38. 0.022 — 0.76 wt% C : hypoeutectoid (less than eutectoid) alloy.
HYPOEUTECTOID ALLOYS
F9.29
F9.30
0.022 — 0.76 wt% C : hypoeutectoid (less than eutectoid) alloy.
In cooling to point d, most of the small α particles (proeutectoid ferrite) will form along the original γ grain boundaries.
As the temperature is lowered just below the eutectoid, all the γ (having the eutectoid composition) will transform to pearlite (eutectoid ferrite ) ferrite. The fraction of pearlite, Wp:
(9.18)
F9.31

39. eutectic reaction (at 4.30 wt% C and 1147°C) :
eutectoid reaction ( at 0.76wt% C and a temperature of 727 °C) :
(fundamental to the heat treatment of steels)
Ferrous alloys are those in which iron is the prime component, but carbon as well as other alloying elements may be present. Based on carbon content, there are three types: iron, steel, and cast iron. Pure iron: less than wt% C, ferrite phase; Steels: between and 2.14 wt% C (rarely exceed 1.0 wt%) , consists of both α and Fe3C phases ; Cast irons: 2.14 —6.70 wt% C( normally less than 4.5 wt% C).

40. The fraction of proeutectoid α , W α,
(9.19)
Fractions of both total α ( eutectoid and proeutectoid) and cementite are determined using the lever rule.
F9.32
F9.33
HYPEREUTECTOID ALLOYS
Containing between 0.76 and 2.14 wt% C.
Proeutectoid cementite as the temperatue is lowered through the eutectoid to point i , all remaining austenite of eutectoid composition is converted into pearlite ; resulting pearlite and proeutectoid cementite as microconstituents
F9.29
F9.30

41. Fractions of pearlite Wp and proeutectoid cementite WFe3C‘
(9.20)
(9.21)

42. (c). NONEQUILIBRIUM COOLING
In this discussion, it has been assumed that conditions of metastable equilibrium have been continuously maintained; thatis, sufficient time has been allowed at each new temperature for any necessary adjustment in phase compositions and relative amounts as predicted from the Fe-Fe3C phase diagram. In most situations these cooling rates are impractically slow and really unnecessary; in fact, on many occasions nonequilibrium conditions are desirable.

43. (d). THE INFLUENCE OF OTHER ALLOYING ELEMENTS
Two nonequilibrium effects of practical importance are (1) the occurrence if phase changes or transformations at temperatures other than those predicted by phase boundary lines on the phase diagram, and (2) the existence at room temperature of nonequilibrium phases that do not appear on the phase diagram.
(d). THE INFLUENCE OF OTHER ALLOYING ELEMENTS
Alterations of the positions of phase boundaries and the shapes of the phase fields
One of the important changes : shift in position of the eutectoid with respect to temperature and to carbon concentration
F9.34
F9.35

44. 8-IV. Ceramic Phase Diagrams
Binary phase diagrams, frequently two components share a common element, e.g., Oxygen in binary oxide ceramics.
F12.24
F9.2
A. The Al2O3-Cr2O3 system
Isomorphous, similar to copper-nickel phase diagram (Figure 9.2a).
The solid solution is a subsitiutional one: both aluminum and chromium ions have the same charge, similar radii (0.053 and nm, respectively,and both Al2O3 and Cr2O3 have the same crystal structure(HCP).

45. B. The MgO-Al2O3 System
F12.25
F9.20
Similar to the lead-magnesium diagram (Figure9.20), there exists an intermediate phase, or better a compound called spinel(尖晶石), which has the chemical formula MgAl2O4 (or MgO-Al2O3) (鋁鎂尖晶石)
There is a range of compositions over which spinel is a stable compound.
Spinel is nonstoichiometric for other than the 50 mol% Al2O3-50 mol% MgO composition.
Limited solubility of Al2O3 in MgO due primarily to the differences in charge and radii of the Mg2+ and Al3+ ions (0.072 versus nm)
#88

46. C. The ZrO2-CaO system
F12.26
The compound CaZrO3 contains 31wt% CaO (50 mol% CaO ).
One eutectic(2250℃ and 23wt% CaO) and two eutectoid (1000℃ and 2.5wt% CaO, and 850 ℃ and 7.5wt% CaO) reactions are found for this system
Three different crystal structures exist: tetragonal, monoclinic, and cubic.

47. Pure ZrO2 experiences a tetragonal-to-monoclinic phase transformation at about 1150℃. A relatively large volume change resulting in the formation of cracks that render a ceramic ware useless. This problem is overcome by ‘stabilizing’ the zirconia by adding between about 3 and 7 wt% CaO: above about 1000 ℃ both cubic and tetragonal phases will be present. Upon cooling to room temperature under normal cooling conditions, the monoclinic and CaZr4O9 phases do not form (as predicted from the phase diagram); consequently, the cubic and tetragonal phases are retained, and crack formation is circumvented. Partially stabilized zirconia, or PSZ.

48. Yttrium oxide (Y2O3) and magnesium oxide are also used as stabilizing agents.
For higher stabilizer contents, only the cubic phase may be retained at room temperture; such a material is fully stabilized.
D. The SiO2- Al2O3 system
The polymorphic form of silica at these temperatures: cristobalite.
Silica and alumina are not mutually soluble: absence of terminal solid solutions
Intermediate compound: mullite, 3Al2O3-2SiO2, mullite melts incongruently at 1890℃.
A single eutectic exists at 1587℃ and 7.7 wt% Al2O3
F12.27