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Phase Diagrams
A general overview
Hume Rothery Seminar
Derby, Jan. 17th 2017
Klaus Hack
GTT-Technologies
GTT-Technologies
Contents
Practical use of Phase Diagrams
Binary Systems
Ternary Systems
Family of Phase Diagrams
Multi-component isopleth sections
Zero Phase Fraction lines
Phase Diagrams with additional info
GTT-Technologies
Practical cases of phase
diagram applications
GTT-Technologies
Precipitation Hardening in
Noble Metal Alloy Systems
dental prosthesis based on noble metal alloys
gold band bridge (Etruscan)
ca. 400 bc
modern dental prosthesis
with ceramics coating
mechanical properties are crucial for the application of
noble metal alloys as dental prosthesis
GTT-Technologies
Precipitation Hardening in
Noble Metal Alloy Systems
Alloy compositions and Vickers hardness
Au Pd Pt Ag Sn Ir Härte (HV)
81,5 - 16 - 2 0,5 85
81,8 15 - - 3 0,2 200
63 - 15 20 2 - 87
62 15 - 20 3 - 138
80,2 13,5 4 - 2,1 0,2 180
GTT-Technologies
Precipitation Hardening in
Noble Metal Alloy Systems
micro graph for alloy 1: phase diagram near for alloy 1:
GTT-Technologies
Precipitation Hardening in
Noble Metal Alloy Systems
micro graph for alloy 2: phase diagram near for alloy 2:
GTT-Technologies
Reduction of Refractory Wear
GTT-Technologies
Reduction of Refractory Wear
GTT-Technologies
Reduction of Refractory Wear
GTT-Technologies
Unary System
GTT-Technologies
Example: Fe
GTT-Technologies
Binary System
GTT-Technologies
Example: Pb-Sn
Liquid
FCC_a1 BCT_a5
FCC_a1 + BCT_a5
FCC_a1 + Liquid Liquid + BCT_a5
GTT-Technologies
Example: Pb-Sn
Liquid
FCC_a1 BCT_a5
GTT-Technologies
Example: Pb-Sn
GTT-Technologies
Example: Pb-Sn
GTT-Technologies
Example: Pb-Sn
LIQ
UID
FC
C_a1
BC
T_a5
(1-x) Pb + x Sn
Phase composition
mole fract. Sn
T(K
)
0 0.20 0.40 0.60 0.80 1.00
300
350
400
450
500
550
600
650
GTT-Technologies Example: Pb-Sn
GTT-Technologies
A more complex case: Fe-Ni
L12_FCC
FCC_A1
BCC_A2
BCC_A2
LIQUID
TC
molefraction Ni
T /
[K
]
0 .2 .4 .6 .8 1
300
600
900
1200
1500
1800
Chemical and magnetic ordering !
GTT-Technologies Printed Compilations
• Early compilations by M. Hansen,
R.P. Elliott, F.A. Shunk, W.G.
Moffat
• Succeeded by
„Massalski“
GTT-Technologies
Ternary System
GTT-Technologies
Example: Fe-Co-Cr (isotherm)
GTT-Technologies
Example: Fe-Co-Cr (isotherm)
GTT-Technologies
Example: Fe-Co-Cr (isotherm)
GTT-Technologies
Printed Compilations
SGTE Landolt-
Börnstein Volumes
GTT-Technologies
Family of Phase Diagrams
GTT-Technologies
Copyright by GTT 2016
0i i i iSdT VdP n d q d Gibbs-Duhem:
i i i idU TdS PdV dn dq
N-Component System (A-B-C-…-N)
S
V
nA
nB
nN
T
-P
µA
µB
µN
Extensive
variables Corresponding
potentials
jqi
iq
U
iq
GTT-Technologies
Copyright by GTT 2016
- Type 1 or Potential Diagrams:
Two potentials, Φi vs Φj.
- Type 2 or Mixed Diagrams:
One potential and one ratio of conjugate extensive properties, Φi vs QΦ
j/QΦ
k.
- Type 3 or Extensive Property Diagrams:
Two ratios of conjugate extensive properties,
QΦi/Q
Φk vs QΦ
j/QΦ
k
Only three types of phase diagrams
GTT-Technologies
Copyright by GTT 2016
Interrelationship of corresponding type 1, type 2, type 3 phase
diagrams. (Φ4, Φ5 , ... are held constant; Φ3 is unspecified)
Pelton and Schmalzried, 1973
GTT-Technologies
Copyright by GTT 2016
Phase diagram family for the binary system Fe-C, P=const.
Type 1 Type 2
Type 3 Type 2
GTT-Technologies
Copyright by GTT 2016
Isopleth sections
and
Zero Phase Fraction lines
GTT-Technologies
Copyright by GTT 2016
How to handle such a diagram ?
The method of Zero Phase Fraction lines John Morall et al., since 1984
, rest Fe
GTT-Technologies
Copyright by GTT 2016
A simple ternary with three terminal solutions
C
A
B
GTT-Technologies
Copyright by GTT 2016
… including tie-lines
A
C B
GTT-Technologies
Copyright by GTT 2016
… including 10%-lines
A
C B
GTT-Technologies
Copyright by GTT 2016
… showing zero-phase fraction lines
A
C B
GTT-Technologies
Copyright by GTT 2016
Some generalisations
The inside-outside
feature
The crossover
feature
GTT-Technologies
Copyright by GTT 2016
More generalisations
The number
of phases
feature
NOTE: n must NOT be ZERO !
n
n + 1
n + 2
n + 1
GTT-Technologies
Copyright by GTT 2016
ZPF-lines are a set of phase boundaries,
that mark the appearance of the same phase
GTT-Technologies
Copyright by GTT 2016
ZPF-lines start and end on coordinate axes
or else form a closed loop
GTT-Technologies
Copyright by GTT 2016
Phase Diagrams
with
additional information
GTT-Technologies The Fe-C diagram
0.001
0.001
0.01
0.01
0.1
0.1
1
1
Liquid
FCC_A1
BCC_A2
BCC_A2Liquid + C_Graphit
FCC_A1 + C_Graphit
BCC_A2 + C_Graphit
Fe - C
1 atm, C(s) iso-activities
C/(Fe+C) (mol/mol)
T(C
)
0 0.05 0.1 0.15 0.2 0.25
300
500
700
900
1100
1300
1500
1700
1900
Liquid
FCC_A1
BCC_A2
BCC_A2Liquid + C_Graphit
FCC_A1 + C_Graphit
BCC_A2 + C_Graphit
Fe - C
C/(Fe+C) (mol/mol)
T(C
)
0 0.05 0.1 0.15 0.2 0.25
300
500
700
900
1100
1300
1500
1700
1900
GTT-Technologies
1e-25 1e-25
1e-201e-20
1e-15
1e-15
1e-10
1e-10
1e-5
1e-5
1e.-4
1e-3
1e-3
1e-2
0.21
0.21
1
1
1e-9
1e-9
1e-8
1e-7
1e-6
1e-6
1e-5
1e-5
1e-7
1e-8
1e-6
1e-2
Fe - O
1 atm, O2(g) isobars (atm)
O/(Fe+O) (mol/mol)
T(C
)
0 0.1 0.2 0.3 0.4 0.5 0.6
300
500
700
900
1100
1300
1500
1700
1900
The Fe-O diagram
liq metal + liq slag
BCC_a2 + liq slag
BCC_a2 + Wustite
BCC_a2 + Magnetite
FCC_a1 + Wustite
Hem
atit
e
GTT-Technologies
Summary
• Phase diagrams are of technological
importance, both in materials development
and application
• Public sources of Phase Diagrams provide
information on binary and ternary systems
• CALPHAD type calculations are not
restricted in no. of components but require
new method of reading ZPF lines
• Isobars or isoactivity lines can be added
Recommended