When combining two elements, the main questions are:
What is the resulting equilibrium state?
If we specify:
The composition (e.g., wt% Cu - wt% Ni)
The temperature (T)
Then:
How many phases form?
What is the composition of each phase?
What is the amount of each phase?
Solubility Limit
Definition: Maximum concentration for which only a single phase solution exists.
Example: Sugar in water at 20°C.
Answer: 65 wt% sugar.
At 20°C, if C < 65 wt% sugar: syrup (single phase)
At 20°C, if C > 65 wt% sugar: syrup + sugar (two phases)
Phase Diagram:
Illustrates the solubility limit of sugar in water as a function of temperature.
L (liquid solution, i.e., syrup) exists below the solubility limit.
L (liquid) + S (solid sugar) exists above the solubility limit.
Solutions vs. Mixtures
Solution: Solid, liquid, or gas, single phase.
Mixture: More than one phase.
Components and Phases
Components: The elements or compounds present in the alloy (e.g., Al and Cu).
Phases: The physically and chemically distinct material regions that form (e.g., α and β).
Altering Temperature (T) and Composition (C)
Altering T can change the number of phases: path A to B.
Altering C can change the number of phases: path B to D.
Example (Water-Sugar System):
A (20°C, C = 70 wt% sugar): 2 phases
B (100°C, C = 70 wt% sugar): 1 phase
D (100°C, C = 90 wt% sugar): 2 phases
One-Component (or Unary) Phase Diagrams
Example: Pressure-temperature phase diagram for H₂O.
Shows the conditions (pressure and temperature) at which different phases (solid, liquid, vapor) are stable.
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 = 0°C).
Similarly, point 3, the intersection with the liquid-vapor boundary, represents the boiling point (T = 100°C).
Simple System (e.g., Ni-Cu solution)
Ni and Cu are totally soluble in one another for all proportions.
Hume-Rothery Rules: Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii, suggesting high mutual solubility.
Ni: FCC, Electronegativity = 1.9, r (nm) = 0.1246
Cu: FCC, Electronegativity = 1.8, r (nm) = 0.1278
Phase Diagrams
Definition: Shows the relationships among temperature T, composition C, and phases present in a particular alloy system at equilibrium.
For this course:
Binary systems: just 2 components.
Independent variables: T and C (P = 1 atm is almost always used).
Example: Phase Diagram for Cu-Ni system.
2 phases: L (liquid), α (FCC solid solution).
3 different phase fields: L, L + α, α.
Cu-Ni Phase Diagram
The Cu-Ni 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 100 wt% Ni.
Rules for Phase Diagrams
Rule 1: If we know T and C_0, then we know which phase(s) is (are) present.
Examples:
A(1100°C, 60 wt% Ni): 1 phase: α
B(1250°C, 35 wt% Ni): 2 phases: L + α
Rule 2: If we know T and C_0, then we can determine the composition of each phase in the 2-phase region.
Examples: Consider C_0 = 35 wt% Ni
At TA = 1320°C: Only Liquid (L) present, CL = C_0 = 35 wt% Ni
At TB = 1250°C: Both α and L present, CL = C{liquidus} = 32 wt% Ni, C\alpha = C_{solidus} = 43 wt% Ni
At TD = 1190°C: Only Solid (α) present, C\alpha = C_0 = 35 wt% Ni
Rule 3: If we know T and C_0, then can determine the weight fraction of each phase.
Examples:
At TA: Only Liquid (L) present, WL = 1.00, W_\alpha = 0
At TD: Only Solid (α) present, WL = 0, W_\alpha = 1.00
Note: Intermetallic compound exists as a line on the diagram - not an area - because of stoichiometry (i.e. composition of a compound is a fixed value).
Eutectoid Diagram
Eutectoid - one solid phase transforms to two other solid phases (3 solid phases NO Liq.)
Peritectic Diagram (Ag - Pt)
Peritectic - liquid and one solid phase transform to a second solid phase
Phase Diagram Vocabulary
Phase Boundaries
Liquidus
Solidus
Solvus
Composition
Temperature
Alloy
Eutectic/Eutectoid as an adjective
Hypoeutectic alloy
Hypereutectic alloy
Proeutectic Phase
Eutectic, Eutectoid, and Peritectic Transformations
Eutectoid: One solid phase transforms to two other solid phases S2 \rightarrow S1 + S3 (e.g., \gamma \rightarrow \alpha + Fe_3C for Fe-C, 727°C, 0.76 wt% C).
Eutectic: Liquid transforms to two solid phases L \rightarrow \alpha + \beta (e.g., for Pb-Sn, 183°C, 61.9 wt% Sn).
Peritectic: Liquid and one solid phase transform to a second solid phase S1 + L \rightarrow S2 (e.g., \delta + L \rightarrow \gamma for Fe-C, 1493°C, 0.16 wt% C).