2. Phase Diagrams
melting / production process / alloying (strength, Tm...)
heat treatment
microstructure
material properties
system (e.g. Cu-Ni)
components (pure substances or compounds)
phases (uniform physical/chemical characteristic)
solid solution – solvent + solute
solubility limit=> precipitation
pure materials – 2 phases: liquid + solid

3. Phase Equilibria G=min
G=H-TS
=min
Gibbs free energy:
=f(T,c,p)
internal energy
(bonding enthalpy)
entropy
(disorder of molecules
entropy of mixing)
metastable
stable

4. Phase Equilibrium melting point Tm
phase composition <=> G minimization

5. Cu-x%Ni Phase Diagram (p=const) isomorphous
phase composition
=f (T,c)
liquid phase
Gibbs phase rule
F=K-P+2
(F degrees of freedom
depends on number
of components K and
number of phases P)
liquid+ solid phase
solid phase

6. Equilibrium Cooling first solid nuclei two-phase solidification
polycrystalline solid Cu
%Ni

7. Phase Composition Amounts W WSolid=Wa: length of tie line 100% liquid
from CL to Co
divided by
100% liquid
%Ni

8. Non-Equilibrium Cooling
first solid nuclei
concentration changes in
solid AND liquid phase
required!!
by diffusion
Ni concentration in
solid nuclei remains
high:
low Dsolid
segregation

9. Diffusion
steady state diffusion
flux

10. Non-Steady-State Diffusion Ficks‘s 2nd Law
solution (c(0)=0):
diffusion coefficient:

11. Binary Eutectic Phase Diagrams (Pb-Sn)
liquid phase
a and b
solid solution
solid phase
eutectic reaction
a(18.3%Sn) +b (97.8%Sn )
limited
solubility
%Sn Pb

12. Lamellar Eutectic Microstructure
Tm, similar to pure components, but: two phases!!

13. Sub-Eutectic Microstructure
lead-rich
a phase
eutectic:
white b
dark a

14. Microstructural Examination - Metallography
preparation of cross section
-cutting
-grinding (SiC paper) -polishing (e.g. 1µm diamond suspension)
-etching (selective chemical attack of grains/grain boundaries)
optical microscopy
electron microscopy (transmission (TEM) or scanning (SEM))

15. Metallography (SEM) detector electron beam secondary electrons
specimen

16. Binary Eutectic Phase Diagrams
a phase
solvus line:
precipitation
of b phase Pb
%Sn

17. Intermetallic Phases/Compounds (e.g. ceramics)
CaZr4O9

18. The Iron-Carbon Phase Diagram
peritectic subsystem
Steel
Cast Iron
bcc d ferrite
eutectic system
eutectoid subsystem
fcc g austenite
Fe3C precipitation
ferrite precipitation
bcc a ferrite
cementite Fe3C

19. Hypoeutectoid Steels (CC<0.76%) ( hypereutectoid)
Ck45 Cc=0.45%
dark
pearlite:
lamellae
of Fe3C and
ferrite
light
a ferrite

20. Hypoeutectoid Steels (CC<0.76%) ( hypereutectoid)
Ck15 Cc=0.15%
dark
pearlite:
light
a ferrite