THERMODYNAMIC ASSESSMENT OF THE TI–AL–NB, TI–AL–CR, AND TI–AL–MO SYSTEMS By ...

233 Pages·2009·6.27 MB·English

THERMODYNAMIC ASSESSMENT OF THE TI–AL–NB, TI–AL–CR, AND
TI–AL–MO SYSTEMS
By
DAMIAN M. CUPID
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2009
1
(cid:176)c 2009 Damian M. Cupid
2
This dissertation is dedicated to Samuel Cox, who unfortunately could not be there till the
end.
3
ACKNOWLEDGMENTS
I would first like to acknowledge my advisors, Prof. Hans-Ju¨rgen Seifert and Prof.
Fereshteh Ebrahimi. Without their help, advice, and encouragement, this work would not
be possible. A special thanks is extended to Dr. Olga Fabrichnaya, who has taught me
everything I know about thermodynamic optimization. I thank also my past and present
committee members: Prof. Phillpot, Prof. Sigmund, Prof. Sinnott, and Prof. Lear.
I acknowledge all members of the research group in Florida: Orlando Rios, Mike
Kessler, and Sonalika Goyel. Their experimental work was tremendously helpful. I also
acknowledge the undergraduate students: Jonah Klemm-Toole, Daniel Heinz, and Tabea
Wilk, who participated at various stages in this project.
Members of the research group at Freiberg University of Mining and Technology also
require special acknowledgement: Frau Galina Savinykh and Mario Kriegel and Dmytro
Pavlyuchkov. Mario Kriegel deserves special attention as he worked intensively on the
optimization of the Ti–Al–Cr system.
I am grateful to my friends in Florida and in Germany. They have made my stay on
both sides of the Atlantic memorable.
Last, I would like to deeply acknowledge my parents. Without their support along
every step of the way, this would be impossible.
This work was supported by the University of Florida College of Engineering Alumni
Fellowship and by the NSF/AFOSR under grant number DMR-0605702.
4
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
CHAPTER
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 BACKGROUND AND THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1 Thermodynamic Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1.1 Modeling of the Pure Elements . . . . . . . . . . . . . . . . . . . . . 28
2.1.2 Modeling of Stoichiometric Phases . . . . . . . . . . . . . . . . . . . 31
2.1.3 Modeling of Substitution Solutions . . . . . . . . . . . . . . . . . . . 31
2.1.3.1 Extrapolation methods . . . . . . . . . . . . . . . . . . . . 33
2.1.4 Modeling of Ordered Phases – The Compound Energy Formalism . 35
2.1.5 Phases with Order–Disorder Transformations . . . . . . . . . . . . . 37
2.2 Thermodynamic Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.1 Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2.2 Theoretical Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2.3 Gibbs Free Energy Minimization . . . . . . . . . . . . . . . . . . . . 40
2.2.4 Optimization Method: The Least Squares Method . . . . . . . . . . 41
3 REVIEW OF THE Ti–Al–Nb SYSTEM . . . . . . . . . . . . . . . . . . . . . . 48
3.1 Phases in the Ti–Al–Nb System . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Experimentally Determined Phase Equilibria in the Ti–Al–Nb System . . . 50
3.2.1 The Liquidus Surface . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.2 Isothermal Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.3 Vertical Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3 Thermodynamic Descriptions of the Ti–Al–Nb System . . . . . . . . . . . 52
3.3.1 Thermodynamic Description of Kattner and Boettinger . . . . . . . 53
3.3.2 Thermodynamic Description of Servant and Ansara . . . . . . . . . 54
3.3.2.1 Reasons for re-optimization . . . . . . . . . . . . . . . . . 54
3.3.3 Thermodynamic Description of Witusiewicz et al. . . . . . . . . . . 56
3.3.3.1 Thermodynamic description of the Ti–Al system . . . . . 56
3.3.3.2 Thermodynamic description of the Al–Nb system . . . . . 58
3.3.3.3 Thermodynamic Description of the Ti–Al–Nb system . . . 59
5
4 KEY EXPERIMENTAL DATA FOR OPTIMIZATION . . . . . . . . . . . . . . 76
4.1 Tie Line Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 Alloy 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2.1 DTA Peak Analysis for Alloy 11 . . . . . . . . . . . . . . . . . . . . 78
4.3 Alloy 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3.1 DTA Peak Analysis for Alloy 12 . . . . . . . . . . . . . . . . . . . . 80
5 RE-OPTIMIZATION OF THE Ti–Al–Nb SYSTEM . . . . . . . . . . . . . . . . 97
5.1 Unary Data and Binary Sub-Sections . . . . . . . . . . . . . . . . . . . . . 97
5.2 Thermodynamic Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2.1 Optimization Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.3 Selection of Thermodynamic Parameters . . . . . . . . . . . . . . . . . . . 99
5.3.1 The Sigma phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3.2 The Delta Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.3.3 The Beta Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.3.4 The Gamma Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3.5 The Ordered Beta Phase . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3.6 The Disordered Alpha and Ordered Alpha–2 Phases . . . . . . . . . 104
5.3.7 The Liquid Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6 RESULTS OF THE RE-OPTIMIZATION . . . . . . . . . . . . . . . . . . . . . 112
6.1 Liquidus and Solidus Projections . . . . . . . . . . . . . . . . . . . . . . . 112
6.2 Isothermal Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.3 Vertical Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.4 Phase Fraction Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7 THE Ti-Cr SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.1 Phase Equilibria in the Ti–Cr System . . . . . . . . . . . . . . . . . . . . . 125
7.2 Thermodynamic Descriptions of the Ti–Cr System . . . . . . . . . . . . . . 127
7.2.1 Lattice Stability of Pure Cr . . . . . . . . . . . . . . . . . . . . . . 127
7.2.2 Number of Laves Phases Modeled . . . . . . . . . . . . . . . . . . . 128
7.2.3 Modeling of the Laves Phases . . . . . . . . . . . . . . . . . . . . . 128
7.2.4 The Homogeneity Ranges of the Laves Phases . . . . . . . . . . . . 129
7.2.5 The Activity of Cr in the Beta Phase . . . . . . . . . . . . . . . . . 130
7.3 Optimization of the Parameters for the Binary Ti–Cr System . . . . . . . . 131
7.3.1 Selection of Thermodynamic Parameters for the Laves Phases . . . 132
7.3.2 Optimization Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.3.3 Optimized Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8 THE Ti-Al-Cr SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
8.1 Phases in the Ti–Al–Cr System . . . . . . . . . . . . . . . . . . . . . . . . 145
8.2 Experimentally Determined Phase Equilibria . . . . . . . . . . . . . . . . . 146
8.2.1 Isothermal Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6
8.2.2 The Liquidus Surface . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8.3 Critical Assessments of the Ti–Al–Cr System . . . . . . . . . . . . . . . . . 147
8.4 Thermodynamic Descriptions of the Ti–Al–Cr System . . . . . . . . . . . . 148
8.4.1 Thermodynamic Description of Saunders . . . . . . . . . . . . . . . 148
8.4.1.1 Reasons for re-optimization . . . . . . . . . . . . . . . . . 150
8.5 Re-optimization of the Ti–Al–Cr System . . . . . . . . . . . . . . . . . . . 151
8.5.1 Optimization Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.5.1.1 The alpha2 phase . . . . . . . . . . . . . . . . . . . . . . . 151
8.5.1.2 The ternary Ti(Al,Cr)2 laves phase . . . . . . . . . . . . . 152
8.5.1.3 The ternary tau phase . . . . . . . . . . . . . . . . . . . . 153
8.5.1.4 The beta phase . . . . . . . . . . . . . . . . . . . . . . . . 154
8.5.1.5 The ordered beta phase . . . . . . . . . . . . . . . . . . . 154
8.5.1.6 The TiCr2 laves phases . . . . . . . . . . . . . . . . . . . . 155
8.6 Results of the Re-optimization . . . . . . . . . . . . . . . . . . . . . . . . . 155
9 REVIEW OF THE TI-AL-MO SYSTEM . . . . . . . . . . . . . . . . . . . . . . 164
9.1 Binary Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
9.2 Phases in the Ti–Al–Mo System . . . . . . . . . . . . . . . . . . . . . . . . 165
9.3 Review of Critical Assessments in the Region from 0 to 20 at.%Ti . . . . . 167
9.4 Thermodynamic Descriptions of the Ti–Al–Mo System . . . . . . . . . . . 170
10 RE-OPTIMIZATION OF THE AL-MO AND TI-AL-MO SYSTEMS . . . . . . 181
10.1 Review of the Al–Mo System . . . . . . . . . . . . . . . . . . . . . . . . . 181
10.2 Thermodynamic Descriptions for the Al–Mo System . . . . . . . . . . . . . 186
10.3 Re-optimization of the Al–Mo System . . . . . . . . . . . . . . . . . . . . . 186
10.3.1 Optimization Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 187
10.3.2 Selection of Adjustable Parameters . . . . . . . . . . . . . . . . . . 187
10.3.2.1 The beta phase . . . . . . . . . . . . . . . . . . . . . . . . 187
10.3.2.2 The liquid phase . . . . . . . . . . . . . . . . . . . . . . . 188
10.3.2.3 The Al-rich intermetallic phases . . . . . . . . . . . . . . . 188
10.3.2.4 The AlMo3 phase . . . . . . . . . . . . . . . . . . . . . . . 189
10.3.2.5 The (Al) phase . . . . . . . . . . . . . . . . . . . . . . . . 190
10.3.3 The Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
10.4 Re-optimization of the Ti–Al–Mo System . . . . . . . . . . . . . . . . . . . 191
10.4.1 Optimization Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 191
10.4.2 Selection of Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 192
10.4.2.1 The eta phase . . . . . . . . . . . . . . . . . . . . . . . . . 192
10.4.2.2 The beta phase . . . . . . . . . . . . . . . . . . . . . . . . 193
10.4.2.3 The delta phase . . . . . . . . . . . . . . . . . . . . . . . . 193
10.4.3 The Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
11 CONCLUSIONS AND SUGGESTED FUTURE WORK . . . . . . . . . . . . . 204
11.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
11.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
7
A THERMODYNAMIC PARAMETERS FOR THE TI-AL-NB SYSTEM . . . . . 209
B THERMODYNAMIC PARAMETERS FOR THE TI-AL-CR SYSTEM . . . . . 214
C THERMODYNAMIC PARAMETERS FOR THE TI-AL-MO SYSTEM . . . . 217
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
8
LIST OF TABLES
Table page
3-1 Phases in the Ti–Al–Nb system. . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3-2 Thermodynamic modeling of the phases used in the description of Kattner and
Boettinger [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3-3 Thermodynamic modeling of the phases in the Ti–Al–Nb system of Servant and
Ansara [10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3-4 Thermodynamic modeling of the phases in the Ti–Al–Nb system of Witusiewicz
et al. [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4-1 Key experimental works in the Ti–Al–Nb system . . . . . . . . . . . . . . . . . 83
4-2 Tie line and tie triangle data for alloys A2, A3, and A133 that were used for
the optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4-3 Transition temperatures for alloy 11 and alloy 12. . . . . . . . . . . . . . . . . . 96
5-1 Crystal structure of the σ phase [135] . . . . . . . . . . . . . . . . . . . . . . . . 106
7-1 Phases in the Ti–Cr system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7-2 Homogeneity range of the Laves phases determined by Chen et al. [148]. . . . . 137
7-3 Crystal structure of the α–TiCr Laves phase. . . . . . . . . . . . . . . . . . . . 138
2
7-4 Crystal structure of the β–TiCr Laves phase. . . . . . . . . . . . . . . . . . . . 139
2
7-5 Crystal structure of the γ–TiCr Laves phase. . . . . . . . . . . . . . . . . . . . 140
2
7-6 Data on the Laves phases that were used for the optimization. . . . . . . . . . . 141
8-1 Stable solid phases in the Ti–Al–Cr system. . . . . . . . . . . . . . . . . . . . . 156
9-1 Stable solid phases in the Ti–Al–Mo system. . . . . . . . . . . . . . . . . . . . . 175
10-1 Invariant reactions in the Al–Mo system which were accepted for the optimization
based on a critical evaluation of the available literature. . . . . . . . . . . . . . . 196
A-1 Thermodynamic Description for the Ti–Al–Nb System . . . . . . . . . . . . . . 209
B-1 Thermodynamic Description for the Ti–Al–Cr System . . . . . . . . . . . . . . . 214
C-1 Thermodynamic Description for the Ti–Al–Mo System . . . . . . . . . . . . . . 217
9
LIST OF FIGURES
Figure page
2-1 Schematic of the CALPHAD method [62]. . . . . . . . . . . . . . . . . . . . . . 44
2-2 The contribution to the excess Gibbs free energy of mixing from the first four
terms in the Redlich-Kister polynomial. . . . . . . . . . . . . . . . . . . . . . . . 45
2-3 Graphical representation of the A) Kohler, B) Colinet, and C) Muggianu and
D) Toop ternary extrapolation methods. In all diagrams, the open circle represents
a point of ternary composition (x , x , x ). The filled squares show the points
i j k
on the i–j binary which will make a contribution to the Gibbs free energy of
the ternary composition. The Kohler and Muggianu extrapolation methods use
only one point along the i–j binary whereas the Colinet extrapolation method
uses two points along the i–j binary. One point gives the mole fraction of i and
the other point gives the mole fraction of j that will be used. Therefore, in the
Colinet method, xbin+xbin (cid:54)= 1. In Toop extrapolation, the points along the i–k
i j
and j–k binaries are chosen at constant x , but the point along the i–j binary
k
is chosen using in the same way as the Kohler method. . . . . . . . . . . . . . . 46
2-4 The surface of reference for a hypothetical compound (A,B) (C,D) plotted
p q
above the composition square. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3-1 The calculated A) Ti–Al, B) Nb–Al, and C) Ti–Nb constituent binary systems
used in the thermodynamic dataset of Kattner and Boettinger. Figures taken
from [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3-2 Calculated liquidus using the thermodynamic description of Kattner and Boettinger.
Figure taken from [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3-3 The calculated A) Ti–Al, B) Nb–Al, and C) Ti–Nb constituent binary systems
used in the thermodynamic dataset of Servant and Ansara [10]. . . . . . . . . . 65
3-4 Isothermal section at 1273 K calculated using the thermodynamic description
of Servant and Ansara [10]. The experimental data identified as [1992Men] and
[1998Hel] refer to the works of Menon et al. [109] and Hellwig et al. [101] respectively. 66
3-5 Isothermal section at 1373 K calculated using the thermodynamic description
of Servant and Ansara [10]. The experimental data identified as [1999Eck] and
[2002Leo] refer to the works of Eckert et al. [108] and Leonard et al. [107] respectively. 67
3-6 Isothermal section at 1473 K calculated using the thermodynamic description
of Servant and Ansara [10]. The experimental data identified as [1992Men], [1995Zdz],
and [1998Hel] refer to the works of Menon et al. [109], Zdziobek et al. [13], and
Hellwig et al. [101] respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
10