1. Solidification and Phase Diagrams
Dr. Siddhalingeshwar I.G.

2. Unit II Chapter 4: Solidification and phase diagrams:
Mechanism of solidification, Homogeneous and heterogeneous nucleation, crystal growth, cast metal structures, Solid solutions, Hume Rothery rules, substitutional and interstitial solid solutions, intermediate phases, Gibbs phase rule, construction of equilibrium diagrams, equilibrium diagrams involving complete and partial solubility, lever rule, Iron carbon equilibrium diagram, description of phases, solidification of steels and cast irons, invariant reactions, Numericals.
07 hours
Chapter 5: Ferrous and Non ferrous materials:
Properties, composition and uses of cast irons and steels, AISI and BIS designation of steels. Aluminum, Magnesium and Titanium alloys. 06
hours
Chapter 6: Heat treatment of metals:
Objectives, Annealing and its types, normalizing, hardening, tempering, austempering, martempering, hardenability, surface hardening methods like carburizing, cyaniding, nitriding, flame hardening and induction hardening; Age hardening of Aluminum -Copper alloys. Time-temperature-transformation (TTT) curves, continuous cooling curves.
06 hours

3. Chapter 4: Lesson Schedule
01. Solid solutions, types of solid solutions, Hume Rothery Rules for complete miscibility. 02. Gibb’s phase rule and its applications. 03. Cooling curves for pure metal, binary solid solution. 04. Binary phase diagrams involving complete and partial solubility. 05. Examples on phase diagram and numerical. 06. Iron-Carbon (Fe-Fe3 C) equilibrium diagram in detail with emphasis on invariant reactions. 07. Microstructure of slowly cooled steels, effect of alloying elements on the Fe-C diagram.

4. The understanding of Science of Solidification is important because it is applied to a wide range of materials from metals and alloys to ceramics to polymers. Solidification is of such importance simply because one of its major practical applications, namely casting, is a very economic method of forming a component. Properties of casting are not easy to control, hence this understanding is important to manipulate the process to achieve desired results.

5. 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.

6. Learning Outcomes
Explain the mechanism of solidification in pure metals and alloys and Distinguish between homogeneous and heterogeneous nucleation.
Calculate critical radius, number of nuclei and driving force for homogeneous nucleation.
Utilize the Gibbs Phase Rule to compute equilibrium number of phases for any given temperature, pressure and number of independent components.
Construct a phase diagram from phase composition data as well as from cooling curves.

7. Learning Outcomes
Given a binary phase diagram, the composition of alloy, its temperature and assuming that the alloy is at equilibrium, compute what phases are present, the composition of the phases, the mass fraction of phases and comment on the solidification phenomenon.
Identify the important phase regions of the Fe-C phase diagram.
Describe the significance of critical cooling rate and explain the factors affecting it.
Explain the various micro constituents of Iron and Steel, their microstructure, characterization, properties and areas of application.
Explain the transformations that take place in the structure of steels and cast iron, and identify the associated microstructure.

8. Why is solidification important?
80% of ALL industry involves a casting or solidification process of a material in various ways;
The initial microstructure of the material forms during the casting or solidification process where the melted alloy becomes a (crystalline) solid;
During the last century, by examining metal alloys with an optical microscope after polishing and etching the surface, it was discovered that the microstructures influenced the material's properties .

10. Classification

11. Why does anything solidify?
The energy of the crystal structure is less than that of the liquid
The difference is the volume free energy DGv
As the solid grows in size, the magnitude of the total volume free energy increases…
But it is a negative value.

12. When solids form in a liquid there is an interface created
The surface free energy, s is associated with this interface
As the solid grows, the total surface free energy increases, and….
It’s a positive value.
The total change in free energy for the system is the sum of the two factors.
DG = 4/3 π r 3DGv π r 2s
The volume free energy goes up as the cube of the radius.
The surface free energy goes up as the square of the radius.

13. Schematic Representation of Solidification

14. Formation of Nuclei
Molecules are always bumping into each other – sometimes they stick
At lower kinetic energies more stick

16. Homogeneous nucleation

17. Gibbs free energy

18. Energies involved in Homogeneous nucleation
The total free energy of the solid-liquid system changes with the size of the solid. The solid is an embryo if its radius is less than the critical radius, and is a nucleus if its radius is greater than the critical radius

19. An interface is created when a solid forms from the liquid

20. Microstructure of rolled and annealed brass (400X magnification)
Dendritic  Structure at the Solid-Liquid Interface of a  Ni-Based Single Crystal
Microstructure of rolled and annealed brass (400X magnification)

22. A solid forming on an impurity can assumed the critical radius with a smaller increase in the surface energy.
Thus, heterogeneous nucleation can occur with relatively low undercoolings.

23. Nucleation in solids. Heterogeneous nucleation can take place at defects like dislocations, grain boundaries, interphase interfaces and free surfaces. Homogeneous nucleation, in defect-free regions, is rare.

24. Grain Size
Solidification caused by homogeneous nucleation occurs suddenly, and only produces a few grains.
In heterogeneous nucleation, solidification occurs on many “seeds”, so the grains are smaller, and more uniform.

25. Growth and Solidification
If a melt is cooled slowly, and the temperature is the same throughout, solidification occurs with equal probability everywhere in the melt. However….
Metals are usually cooled from the container walls – so solidification starts on the walls.

26. Cooling Curves Pouring Temperature.
Superheat – the difference between the pouring temperature and the freezing temperature.
Thermal arrest – constant temperature region on the cooling curve.
Total solidification time – the time it takes to solidify, from the time you pour the mold.
Local solidification time – time to remove the latent heat.

27. Cooling Curve Temperature Pouring Temperature Superheat
Local Solidification Time
Total Solidification Time

28. Solidification of pure metals

30. Solid solutions

31. Solid solutions- Hume-Rothery rules
The Hume-Rothery rules, named after William Hume-Rothery, are a set of basic rules describing the conditions under which an element could dissolve in a metal, forming a solid solution. There are two sets of rules, one which refers to substitutional solid solutions, and another which refers to interstitial solid solutions.
For interstitial solid solutions, the Hume-Rothery rules are:
1. Solute atoms must be smaller than the interstitial sites in the solvent lattice.
2. The solute and solvent should have similar electronegativity.

32. Dr. William Hume-Rothery
The youthful Hume-Rothery read chemistry at Oxford with distinction despite his disability and then worked for his PhD at the Royal School of Mines in London. Upon his return to Oxford with a newly found enthusiasm for work on alloys, he was given a little bench space in the Dyson-Perrins laboratory. In cramped accommodation, he began the long series of investigations into alloy equilibria and the inspired hypotheses which led to the famous Hume-Rothery Rules. 

33. Hume-Rothery rules
For substitutional solid solutions, the Hume-Rothery rules are:
1. The atomic radii of the solute and solvent atoms must differ by no more than 15%.
2. The crystal structures of solute and solvent must match.
3. Complete solubility occurs when the solvent and solute have the same valency. A metal will dissolve a metal of higher valency to a greater extent than one of lower valency.
4. The solute and solvent should have similar electronegativity. If the electronegativity difference is too great, the metals will tend to form intermetallic compounds instead of solid solutions.

34. An example of a substitutional solid solution is found for copper and nickel. These two elements are completely soluble in one another at all proportions.
With regard to the aforementioned rules that govern degree of solubility, the atomic radii for copper and nickel are and nm, respectively,
both have the FCC crystal structure, and
their electronegativities are 1.9 and 1.8 ;
finally, the most common valences are +1 for copper (although it sometimes can be + 2) and +2 for nickel.

36. For interstitial solid solutions, impurity atoms fill the voids or interstices among the host atoms. For metallic materials that have relatively high atomic packing factors, these interstitial positions are relatively small. Consequently, the atomic diameter of an interstitial impurity must be substantially smaller than that of the host atoms.
Carbon forms an interstitial solid solution when added to iron; the maximum concentration of carbon is about 2%.
The atomic radius of the carbon atom is much less than that for iron: nm versus nm.

37. A solid solution is formed when two metals are completely soluble in liquid state and also completely soluble in solid state. In other words, when homogeneous mixtures of two or more kinds of atoms (of metals) occur in the solid state, they are known as solid solutions.
The more abundant atomic form is referred as solvent and the less abundant atomic form is referred as solute.
For example sterling silver (92.5 percent silver and the remainder copper) is a solid solution of silver and copper.
Another example is brass. Brass is a solid solution of copper (64 percent) and zinc (36 percent). In this case copper atoms are solvent atoms whereas zinc atoms are solute atoms

38. Substitutional Solid Solutions:
If the atoms of the solvent or parent metal are replaced in the crystal lattice by atoms of the solute metal then the solid solution is known as substitutional solid solution.
For example, copper atoms may substitute for nickel atoms without disturbing the F.C.C. structure of nickel. In the substitutional solid solutions, the substitution can be either disordered or ordered.

40. In interstitial solid solutions, the solute atom does not displace a solvent atom, but rather it enters one of the holes or interstices between the solvent atoms.
An excellent example is iron-carbon system. In this system the carbon (solute atom) atom occupies an interstitial position between iron (solvent atom) atoms.
Normally, atoms which have atomic radii less than one angstrom are likely to form interstitial solid solutions. Examples are atoms of carbon (0.77 A°), nitrogen (0.71 A°), hydrogen (0.46 A°), Oxygen (0.60 A°) etc.

42. Two types of alloys:
Substitutional: atoms of metals are about the same size and replace each other in metal crystal
Interstitial: atoms of different size. Smaller atoms fit into the spaces between the larger atoms.

43. Phase diagrams

44. Concepts
Phase: A homogenous portion of a system that has uniform physical and chemical characteristics.
Solubility limit: Maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution.
It depends on temperature.
Solubility limit at some temperature is the composition that corresponds to the intersection of the given temperature coordinate and the solubility limit line.

45. Concepts (Cont.)
Examples of phases: Pure material, gas, liquid, or solid solutions, water and ice together (two phases), two polymorphic forms of a solid, e.g., FCC & BCC (two phases).
Heterogeneous systems: Systems consisting of two or more phases.
Microstructure (in metals) is characterized by: Number of phases present, their proportions, manner in which they are distributed or arranged.
Microstructure in alloys depends on alloying element present, their concentrations, and heat treatment.

46. Concepts (Cont.)
Phase equilibrium: A system is at equilibrium if its free energy is at a minimum under some specified combination of temperature, pressure, and composition, i.e., system characteristics do not change with time.
Free energy: It is a function of the internal energy of a system. It is also a function of the randomness or disorder of the atoms or molecules (entropy).
A change in temperature, pressure, and/or composition for a system in equilibrium results in an increase in the free energy and in possible spontaneous change to another state where free energy is lowered.

47. Gibbs' phase rule F=C-P+2
Gibbs' phase rule was proposed by Josiah Willard Gibbs in the 1870s as the equality
F=C-P+2
where P is the number of phases in thermodynamic equilibrium with each other and C is the number of components.
Typical phases are solids, liquids and gases. A system involving one pure chemical is an example of a one-component system. Two-component systems, such as mixtures of water and ethanol, have two chemically independent components.
F is the number of degrees of freedom, which means the number of intensive properties such as temperature or pressure, which are independent of other intensive variables.

48. Josiah Willard Gibbs
The publication of the paper "On the Equilibrium of Heterogeneous Substances" (1874–78) is regarded as a landmark in the development of physical chemistry. In it, Gibbs developed a rigorous mathematical theory for various transport phenomena, including adsorption, electrochemistry, and the Marangoni effect in fluid mixtures. He also formulated the phase rule. Awareness of this rule led to the widespread use of phase diagrams by chemists.

49. Equilibrium phase diagram
Phase diagram: Equilibrium or constitutional diagrams: It represents the relationships between temperature and the compositions and the quantities of phases at equilibrium.
Phase diagrams for binary alloy (contains two components) is the simplest.
External pressure is assumed constant (atmospheric pressure).

50. Pressure-temperature diagram for Water
Unary phase diagram
Pressure-temperature diagram for Water
The simplest phase diagrams are pressure-temperature diagrams of a single simple substance, such as water.
The axes correspond to the pressure and temperature.
The phase diagram shows, in pressure-temperature space, the lines of equilibrium or phase boundaries between the three phases of solid, liquid, and gas.
Three externally controllable parameters that will affect phase structure: temperature, pressure, and composition
The simplest type of phase diagram to understand is that for a one-component system, in which composition is held constant

52. Unary phasediagram

53. Ex: Phase Diagram: Water-Sugar System
Question: What is the
solubility limit at 20C?
Answer: 65wt% sugar.
If Co < 65wt% sugar: sugar
If Co > 65wt% sugar: syrup + sugar.
• Solubility limit increases with T: e.g., if T = 100C,
solubility limit = 80wt% sugar.

54. • Changing T can change # of phases: path A to B.
• Changing Co can change # of phases: path B to D.
• water- sugar
system

55. Binary isomorphous systems
Example: Copper-Nickel phase diagram
Isomorphous: Complete liquid and solid solubility of the components.
Three different fields (delimited by phase boundary lines):
Solid
Liquid
Solid + liquid

56. Binary isomorphous systems (Cont.)
Nomenclature:
For metallic alloys, solid solutions are designated by lowercase Greek letters.
Liquidus line.
Solidus line.
Thermal arrest occurs at the melting temperature of the pure metal (liquidus and solidus lines intersect).
For any composition other than pure components, melting occur over a temperature range (between liquidus and solidus line). Both solids and liquid phases are in equilibrium in this temperature range.

57. Interpretation of phase diagrams
Available information from phase diagrams:
Present phases.
Phase composition.
Percentage (or fractions) of each phase.
Determination of phases present: Locate the temperature-composition point on the phase diagram and note the phase(s) with which the corresponding phase field is labeled.
Determination of phase composition:
Locate temperature-composition point on the phase diagram.
If one phase is present: phase composition is the given alloy composition.

58. Melting Temperature of B
Two Component (Binary) Phase Diagram for completely soluble elements or compounds
Melting
Temperature of A
Liquid
Temperature, °C
Liquid +
Solid a
Look at the melting temperature for each element
Alloying element A with element B drops the melting temperature
Solid a
Components
Melting Temperature of B
Percent A by weight 10 20 30 40 50 60 70 80 90
100
Percent B by weight
100 90 80 70 60 50 40 30 20 10

59. Two Component (Binary) Phase Diagram: Ni - Cu
1700
1000
1100
1200
Nickel - Copper Alloy
1600
Liquid
Liquidus Line
1500
1455°C
1400
Temperature, °C
1300
Liquid +
Solid a
Cu and Ni are completely soluble because the electronegativities, radii, crystal structure (FCC), etc. are the similar.
Solidus Line
Solid a
1084°C
Percent Ni by weight 10 20 30 40 50 60 70 80 90
100
Percent Cu by weight
100 90 80 70 60 50 40 30 20 10

60. Binary Phase Diagram for insoluble elements or compounds
Liquid A + B
Temperature. °C
Liquid + A
Liquid + B
Solid A + B
Composition of A
Composition of B
Actual atomic form will depend
on the composition of formation

61. (1) Number and types of phases
• Rule 1: If we know T and Co, then we know:
--the # and types of phases present.
Cu-Ni phase
diagram
• Examples:

62. Interpretation of phase diagrams (Cont.)
Determination of phase composition if two phases are present:
A tie line (isotherm) is constructed across the two-phase region at the temperature of the alloy (it terminates at the phase boundary lines on either side).
The intersections of the tie line and the phase boundaries on either side are noted.
Perpendiculars are dropped from these intersections to the horizontal composition axis, from which the composition of each of the respective phases is read

63. (2) Composition of phases
• Rule 2: If we know T and Co, then we know:
--the composition of each phase.
Cu-Ni system
• Examples:

64. Interpretation of phase diagrams (Cont.)
Determination of phase amounts (if more than one phase):
Construct a tie line.
Locate the overall alloy composition on the tie line.
Use lever rule (Line segment lengths may be determined by direct measurement from phase diagram or by subtracting compositions as taken from composition axis).
WL = S / (R + S)
W = R / (R + S)

65. The Lever Rule • A geometric interpretation:
• Sum of weight fractions:
• Conservation of mass (Ni):
• Combine above equations:
• A geometric interpretation:

66. (3) Weight fractions of phases
• Rule 3: If we know T and Co, then we know:
--the amount of each phase (given in wt%).
Cu-Ni system
• Examples:
= 27wt%

67. Development of microstructure (equilibrium cooling)
With continuous cooling, both composition and relative amounts of each of the phases will change.
The composition of the liquid and solid solution () phases will follow the liquidus and solidus lines.
The fraction of the solid phase will increase with continued cooling.
The overall alloy composition remains unchanged.

68. Phase diagram: Cu-Ni system.
• System is:
--binary
i.e., 2 components:
Cu and Ni.
--isomorphous
i.e., complete
solubility of one
component in
another; a phase
field extends from
0 to 100wt% Ni.
• Consider
Co = 35wt%Ni.

69. Mechanical Properties: Cu-Ni System
• Effect of solid solution strengthening on:
--Tensile strength (TS)
--Ductility (%EL,%AR)
--Peak as a function of Co
--Min. as a function of Co

70. Binary eutectic systems
Three single-phase regions exist.
Limited solubility of solid phases below certain temperature.
Solvus line separates a region of one solid-phase from region of two solid-phases (vs. solidus).
Eutectic point is an invariant point (fixed).
Eutectic (easy melt) reaction:
L(CE)  (CE) + (CE)

71. Binary eutectic systems (Cont.)
Upon cooling, eutectic reaction is similar to solidification of pure components (i.e., reaction proceeds to completion at a constant temperature). However, products of eutectic reaction are two phases while products for pure component is one phase.
Low-melting-temperature alloys are prepared having near-eutectic compositions.

72. Cu-Ag
system

73. • For a 40wt%Sn-60wt%Pb alloy at 150C, find...
--the phases present:
a + b
--the compositions of
the phases:
Pb-Sn system

74. • For a 40wt%Sn-60wt%Pb alloy at 150C, find...
--the phases present: a + b
--the compositions of
the phases:
Ca = 11wt%Sn
Cb = 99wt%Sn
--the relative amounts
of each phase:
Pb-Sn system

75. Binary eutectic systems (Cont.)
Eutectic microstructure: alternating layers (lamellae) of the two solid phases (atomic diffusion only occur over relatively short distances).
Hypo and hyper-eutectic systems.

76. Microstructure in eutectic systems
• Co < 2wt%Sn
• Result:
--polycrystal of a grains.

77. Microstructure in eutectic systems (Cont.)
• 2wt%Sn < Co < 18.3wt%Sn
• Result:
--a polycrystal with fine
b crystals.
Pb-Sn
system

78. • Result: Eutectic microstructure
• Co = CE
• Result: Eutectic microstructure
--alternating layers of a and b crystals.
Pb-Sn
system

79. Microstructure in eutectic systems (Cont.)
• 18.3wt%Sn < Co < 61.9wt%Sn
• Result: a crystals and a eutectic microstructure
Pb-Sn
system
Adapted from Fig. 9.14, Callister 6e.

80. Hypoeutectic and hypereutectic

81. Peritectic and eutectoid reactions
Eutectic:
One liquid phase  Solid phase(1)+Solid phase(2)
Eutectoid (eutectic-like) reaction:
One solid phase  two solid phases
Peritectic reaction:
Solid phase + Liquid phase  One solid phases
All the above reactions involve three phases at equilibrium.

82. Iron-Carbon system Ferrite ( iron) has BCC structure.
Austenite ( iron) has FCC structure.
Cementite is an intermediate compound.
Carbon is an interstitial impurity in the iron-carbon system.

85. Eutectic
eutectoid
Pearlite and Cementine
Austenite
Ferrite
Pearlite
Pearlite and
Carbide
Steel
Cast iron

87. Definition of structures
Various phases that appear on the Iron-Carbon equilibrium phase diagram are as under:
Austenite
Ferrite
Pearlite
Cementite
Martensite*
Ledeburite

88. Definition of structures
Ferrite is known as α solid solution.
It is an interstitial solid solution of a small amount of carbon dissolved in α (BCC) iron.
stable form of iron below 912 deg.C
The maximum solubility is % C at 723C and it dissolves only % C at room temperature.
It is the softest structure that appears on the diagram.

89. Ferrite
Average properties are:
Tensile strength = 275 MPa;
Elongation = 40 % in 2 in;
Hardness > Rockwell C 0 or > Rockwell B 90

90. Pearlite is the eutectoid mixture containing 0
Pearlite is the eutectoid mixture containing 0.80 % C and is formed at 723°C on very slow cooling.
It is a very fine platelike or lamellar mixture of ferrite and cementite.
The white ferritic background or matrix contains thin plates of cementite (dark).

91. Pearlite
Average properties are:
Tensile strength =827 MPa;
Elongation = 20 % in 2 in.;
Hardness = Rockwell C 20, Rock­well B , or
BHN

92. Austenite is an interstitial solid solution of Carbon dissolved in  (F.C.C.) iron.
Maximum solubility is 2.0 % C at 1130°C.
High formability, most of heat treatments begin with this single phase.
It is normally not stable at room temperature. But, under certain conditions it is possible to obtain austenite at room temperature.

93. Austenite
Average properties are:
Tensile strength = MPa;
Elongation = 10 percent in 2 in.;
Hardness = Rockwell C 40, approx; and
toughness = high

94. Cementite or iron carbide, is very hard, brittle intermetallic compound of iron & carbon, as Fe3C, contains 6.67 % C.
It is the hardest structure that appears on the diagram, exact melting point unknown.
Its crystal structure is orthorhombic.
It is has
low tensile strength (approx. 5,000 psi), but
high compressive strength.

95. Ledeburite is the eutectic mixture of austenite and cementite.
It contains 4.3 percent C and is formed at 1130°C.

96. Martensite - a super-saturated solid solution of carbon in ferrite.
It is formed when steel is cooled so rapidly that the change from austenite to pearlite is suppressed.
The interstitial carbon atoms distort the BCC ferrite into a BC-tetragonal structure (BCT).; responsible for the hardness of quenched steel

97. Various Features of Fe-C diagram
Phases present L
a ferrite
BCC structure
Ferromagnetic
Fairly ductile
Reactions d
BCC structure
Paramagnetic
Peritectic L + d = g
Eutectic L = g + Fe3C
g austenite
FCC structure
Non-magnetic
ductile
Fe3C cementite
Orthorhombic
Hard
brittle
Eutectoid g = a + Fe3C
Max. solubility of C in ferrite=0.022%
Max. solubility of C in austenite=2.11%

98. Three Phase Reactions
Peritectic, at 1490 deg.C, with low wt% C alloys (almost no engineering importance).
Eutectic, at 1130 deg.C, with 4.3wt% C, alloys called cast irons.
Eutectoid, at 723 deg.C with eutectoid composition of 0.8wt% C, two-phase mixture (ferrite & cementite). They are steels.

99. Hypo Eutectoid steel

100. Mat. Sc. & Metallurgy by IGS
Hypereutectoid steel
Mat. Sc. & Metallurgy by IGS

102. Summary
Solidification caused by homogeneous nucleation occurs suddenly, and only produces a few grains.
In heterogeneous nucleation, solidification occurs on many “seeds”, so the grains are smaller, and more uniform.
A solid solution may form when impurity atoms are added to a solid, in which case the original crystal structure is retained and no new phases are formed.
Forsubstitutionalsolidsolutions,impurityatomssubstituteforhostatoms,andappre ciable solubility is possible only when atomic diameters and electronegativities for both atom types are similar, when both elements have the same crystal structure, and when the impurity atoms have a valence that is the same as or less than the host material.
Interstitial solid solutions form for relatively small impurity atoms that occupy interstitial sites among the host atoms.

103. Summary • Phase diagrams are useful tools to determine:
--the number and types of phases,
--the wt% of each phase,
--and the composition of each phase
for a given T and composition of the system.
• Alloying to produce a solid solution usually
--increases the tensile strength (TS)
--decreases the ductility.
• Binary eutectics and binary eutectoids allow for a range of microstructures.

104. More on Phase diagrams –Cambridge University

105. The taller the tree...the deeper the roots..