Fully Miscible Solution

1
Fully Miscible Solution
Simple solution system (e.g., Ni-Cu solution)
Crystal Structure electroneg r (nm)
Ni FCC 1.9 0.1246
Cu FCC 1.8 0.1278

• Both have the same crystal structure (FCC) and
  have similar electronegativities and atomic radii
  (W. Hume Rothery rules) suggesting high mutual
  solubility.

• Ni and Cu are totally miscible at all mixture
  compositions isomorphous

2
Copper-Nickel Binary Equilibrium Phase Diagram

• Solid solutions are typically designated by lower
  case Greek letters a, B, g, etc.
• Liquidus line separates liquid from two phase
  field
• Solidus line separates two phase field from a
  solid solution
• Pure metals have melting points
• Alloys have melting ranges

What do we have? Whats the composition?
3
The Lever Rule

• Draw Tie line connects the phases in
  equilibrium with each other - essentially an
  isotherm

Derived from Conservation of Mass (1) Wa WL
1 (2) WaCa WLCL Co
Let W mass fraction (amount of phase)
Adapted from Fig. 9.3(b), Callister 7e.
4
Example Calculation
tie line
R
S
5
Equilibrium Cooling in a Cu-Ni Binary
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 100 wt Ni.
Consider Co 35 wtNi.
6
Cored vs Equilibrium Phases
Ca changes as we solidify. Cu-Ni case
First a to solidify has Ca 46 wt Ni. Last a
to solidify has Ca 35 wt Ni.
Fast rate of cooling Cored structure
Slow rate of cooling Equilibrium structure
7
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
8
Consider Pb-Sn System
Simple solution system (e.g., Pb-Sn solution)
Crystal Structure electroneg r (nm)
Pb FCC 1.8 0.175
Sn Tetragonal 1.8 0.151
13.7

• W. Hume Rothery Rules
• Atomic size is within 15
• Same electronegativity
• Do not have same crystal structure

Will have some miscibility, but will not have
complete miscibility
9
Binary-Eutectic System
From Greek eut ktos, easily melted
Liquidus
Solidus
Eutectic Point


Solvus
10
Microstructural Evolution in Eutectic
Consider (1) Co lt 2 wt Sn Result --at
extreme ends --polycrystal of a grains
i.e., only one solid phase.
11
Microstructural Evolution in Eutectic

• Consider (2)
• 2 wt Sn lt Co lt 18.3 wt Sn
• Result
• Initially liquid ?
• then ? alone
• finally two phases
• a polycrystal
• fine ?-phase inclusions

12
Microstructural Evolution in Eutectic
Consider (3) Co CE Result Eutectic
microstructure (lamellar structure)
--alternating layers (lamellae) of a and b
crystals.
13
Lamellar Eutectic Structure
14
Microstructural Evolution in Eutectic
Consider (4) 18.3 wt Sn lt Co lt 61.9 wt Sn
T(C)
L Co
wt Sn
Result a crystals and a eutectic microstructure
300

L
Pb-Sn system
L

a
a
b
b
L

200

TE
100

20
60
80
100
0
40
Co, wt Sn
15
Hypoeutectic vs Hypereutectic