Abstract
The availability of reliable materials data is key to the successful design of materials and manufacturing processes. Commercial alloys seldom consist of only two or three elements, but rather may contain a large number of elements for which the needed data are rarely available. The CALPHAD (calculation of phase diagrams method), as implemented in a number of software tools, enables the development of thermodynamic and diffusion databases and the extrapolation of these property data from binary and ternary systems to higher order systems. The computational methods used to calculate thermodynamic and diffusion properties can be invaluable in the design of new materials. In addition, the databases and software tools provide an efficient method of storing a wealth of data and allow efficient retrieval of the needed information. The present paper reviews the development and application of multicomponent thermodynamic and diffusion mobility databases using the CALPHAD method.
Get full access to this article
View all access options for this article.
References
1.
Massalski
T. B.
,
Okamoto
H.
,
Subramanian
P. R.
L. Kacprzak (eds.): ‘Binary alloy phase diagrams’, 2nd edn, Vols. 1-3; 1990, Materials Park, OH, ASM International.
2.
Predel
B.
: ‘Phase equilibria, crystallographic and thermodynamic data of binary alloys’, (ed. 0. Madelung), Vol. 5 ; 1991-1998, Landolt-Börnstein, New Series, Berlin, Springer.
3.‘Phase equilibria diagrams’, Vols. IX—XIV, compiled in the Ceramics Division of NIST , 1992-2004, Westerville , OH , The American Ceramic Society .
4.‘Phase diagrams for ceramists’, Vols. I—VIII, compiled in the Ceramics Division of NIST , 1964-1990, Westerville , OH , The American Ceramic Society .
5.
Villars
P.
,
Prince
A.
and
Okamoto
H.
‘Handbook of ternary alloy phase diagrams’, Vols. 1-10; 1995, Materials Park, OH, ASM International.
6.
Petzow
G.
and
Effenberg
G.
‘Ternary alloys: a compre-hensive compendium of evaluated constitutional data & phase diagrams’,Vols. 1-15;1988-1995,Weinheim,VCHVerlagsgesellschaft.
7.ASM Alloy Phase Diagram Center: available at : www.as-minternational.org/asmenterprise/apd/.
8.Phase Equilibria Diagrams: available at : www.ceramics.org/publications/phase.aspx
9.MSIT Workplace/Phase Diagram Center: available at : www.matport.com/workplace/shop/index.shtml
10.
Gale
W. F.
and
Totemeier
T. C.
‘Smithells metals reference book’ ; 2004 , Amsterdam, Elsevier .
11.
Bakker
H.
,
Bonzel
H. P.
,
Bruff
C. M.
,
Dayananda
M. A.
,
Gust
W.
,
Horvath
J.
,
Kaur
I.
,
Kidson
G. V.
,
LeClaire
A. D.
,
Mehrer
H.
,
Murch
G. E.
,
Neumann
G.
,
Stolica
N.
, and
Stolwijk
N. A.
‘Diffusion in solid metals and alloys’ , (ed.
Martienssen
W.
), Vol. 26 , 747 ; 1990 , Berlin, Springer .
12.Diffusion and Defect Forum: available at : www.scientific.net/DDF/.
13.NIST Diffusion Data Center: available at: http://patapsco.nist.gov/diffusion/ .
14.
Hertz
J.
: J. Phase Equilib ., 1992 , 13 , 450 –458 .
15.
Kaufman
L.
and
Bernstein
H.
‘Computer calculation of phase diagrams with special reference to refractory metals’ ; 1970 , New York , Academic Press .
16.
Saunders
N.
and
Miodownik
A. P.
‘CALPHAD: a comprehen-sive guide'; 1998, Oxford, Pergamon.
17.
Spencer
P. J.
: CALPHAD , 2008 , 32 , (1 ), 1 –8 .
18.J. &# O0C4;gren : J. Phys. Chem. Solids , 1982 , 43 , 421 –430 .
19.J. &# O0C4;gren : J. Phys. Chem. Solids , 1982 , 43 , 385 –391 .
20.
Andersson
J.-O.
and
Agren
J.
J. AppL Phys ., 1992 , 72 , 1350 –1355 .
21.
Jönsson
B.
: ISIJ Int ., 1995 , 35 , 1415 –1421 .
22.
Jönsson
B.
: Z. Metallkd , 1995 , 86 , 686 –692 .
23.
Engstrom
A.
and
Agren
J.
Z. Metallkd , 1996 , 87 , 92 –97 .
24.
Hillert
M.
: Physica B , 1981 , 103B , 31 –40 .
25.
Lukas
H. L.
,
Weiss
J.
and
Henig
E.-T.
CALPHAD , 1982 ,6 , 229 –251 .
26.
Dinsdale
A. T.
: CALPHAD , 1991 , 15 , 317 –425 .
27.
Hildebrand
J. H.
: J. Am. Chem. Soc ., 1929 , 51 , 66 –80 .
28.
Hillert
M.
and
Staffansson
L.-I.
Acta Chem. Scand , 1970 , 24 , 3618 –3626 .
29.
Hillert
M.
and
Agren
J.
Metall. Trans. A , 1985 , 16A , 261 –266 .
30.
Sommer
F.
: Z. Metallkd ., 1982 , 73 , 72 –76 .
31.
Blander
M.
and
Pelton
A. D.
Geochim. Cosmochim. Acta , 1987 , 51 , 85 –95 .
32.
Pelton
A. D.
and
Kang
Y.-B.
Int. J. Mater. Res ., 2007 , 98 , 907 –917 .
33.
Wagner
C.
and
Schottky
W.
Z. phys. Chem. B , 1930 , 11B , 163 –210 .
34.
Bragg
W. L.
and
Williams
E. J.
Proc. Royal Soc. London A, 1934, 145A, 699-730; 1935, 151,
540 –566 .
35.
Redlich
O.
and
Kister
A. T.
Indust. Eng. Chem ., 1948 , 40 , 345 –348 .
36.
Sundman
B.
and
Agren
J.
J. Phys. Chem. Solids , 1981 , 42 , 297 –301 .
37.
Andersson
J.-O.
,
Fernandez Guillermet
A.
,
Hillert
M.
,
Jansson
B.
and
Sundman
B.
Acta Metall , 1986 , 34 , 437 –445
38.
Ansara
I.
,
Chart
T. G.
,
Fernandez-Guillermet
A.
,
Hayes
F. H.
,
Kattner
U. R.
,
Pettifor
D. G.
,
Saunders
N.
and
Zeng
K.
CALPHAD , 1997 , 21 , 171 –218 .
39.
Ferro
R.
and
Cacciamani
G.
CALPHAD , 2002 , 26 , 439 –458 .
40.
Ansara
I.
,
Sundman
B.
and
Willemin
P.
Acta Metall , 1988 , 36 , 977 –982 .
41.
Ansara
I.
,
Dupin
N.
,
Lukas
H. L.
and
Sundman
B.
J. Alloys Compd , 1997 , 247 , 20 –30 .
42.
Kussoffsky
A.
,
Dupin
N.
and
Sundman
B.
CALPHAD , 2001 ,25 , 549 –565 .
43.
Dupin
N.
and
Ansara
I.
Z. Metallkd , 1999 , 90 , 76 –85 .
44.
Abe
T.
and
Sundman
B.
CALPHAD , 2003 , 27 , 403 –408 .
45.
Sanchez
J. M.
,
Ducastelle
F.
and
Gratias
D.
Physica A , 1984 , 128A , 334 –350 .
46.
van de Walle
A.
and
Asta
M.
Modell . Simul Mater. Set Eng ., 2002 , 10 , 521 –538 .
47.
de Fontaine
D.
: Solid State Phys ., 1994 , 47 , 33 –176 .
48.
Oates
W. A.
and
Wenzl
H.
Ser. Mater ., 1996 , 35 , 623 –627 .
49.
Inden
G.
and
Pitsch
W.
in ‘Materials science and technology’, (ed.
Cahn
R. W.
Vol. 5 , 497 –552 ; 1991 , Weinheim , VCH .
50.
van de Walle
A.
,
Asta
M.
and
Ceder
G.
CALPHAD , 2002 , 26 , 519 –553 .
51.
van de Walle
A.
and
Ceder
G.
J. Phase Equilib ., 2002 , 23 , 348 –359 .
52.
Oates
W. A.
,
Zhang
F.
,
Chen
S.-L.
and
Chang
Y. A.
Phys. Rev. B , 1999 , 59B , 11221 –11225 .
53.
Cao
W.
,
Chang
Y. A.
,
Zhu
J.
,
Chen
S.
and
Oates
W. A.
Intermetallics , 2007 , 15 , 1438 –1446 .
54.
Zhu
J.
,
Cao
W.
,
Yang
Y.
,
Zhang
F.
,
Chen
S.
,
Oates
W. A.
and
Chang
Y. A.
Acta Mater ., 2007 , 55 , 4545 –4551 .
55.
Zhang
J.
,
Oates
W. A.
,
Zhang
F.
,
Chen
S-L.
,
Chou
K-C.
and
Chang
Y. A.
Intermetallics , 2001 , 9 , 5 –8 .
56.
de Boer
F. R.
,
Boom
R.
,
Mattens
W. C. M.
,
Miedema
A. R.
and
Niessen
A. K.
‘Cohesion in metals’ ; 1988 , Amsterdam , North-Holland .
57.
Daw
M. S.
,
Foiles
S. M.
and
Baskes
M. I.
Mater. Sci. Rep ., 1993 , 9 , 251 –310 .
58.
Hafner
J.
,
Wolverton
C.
and
Ceder
G.
MRS Bull ., 2006 , 31 , 659 –665 .
59.
Turchi
P. E. A.
,
Abrikosov
I. A.
,
Burton
B.
,
Fries
S. G.
,
Grimvall
G.
,
Kaufman
L.
,
Korzhavyi
P.
,
Rao Manga
V.
,
Ohno
M.
,
Pisch
A.
,
Scott
A.
and
Zhang
W.
CALPHAD , 2007 , 31 , 4 –27 .
60.
Lukas
H. L.
,
Henig
E.-T.
and
Zimmermann
B.
CALPHAD , 1977 , 1 , 225 –236 .
61.
Marquardt
D. W.
: J. Soc. Indust. Appl Math ., 1963 , 11 , 431 –441 .
62.
Königsberger
E.
: CALPHAD , 1991 , 15 , 69 –78 .
63.
Lukas
H. L.
,
Fries
S. G.
and
Sundman
B.
‘Computational thermodynamics, the CALPHAD method’ ; 2007 , New York , Cambridge University Press .
64.
Schmid-Fetzer
R.
,
Andersson
D.
,
Chevalier
P. Y.
,
Eleno
L.
,
Fabrichnaya
O.
,
Kattner
U. R.
,
Sundman
B.
,
Wang
C.
,
Watson
A.
,
Zabdyr
L.
and
Zinkevich
M.
CALPHAD , 2007 , 31 , 38 –52 .
65.
Hillert
M.
: CALPHAD , 1980 , 4 , 1 –12 .
66.
Muggianu
Y.-M.
,
Gambino
M.
and
Bros
L. P.
J. Chim. Phys ., 1975 , 72 , 85 –88 .
67.
Sluiter
M. H. F.
: CALPHAD , 2006 , 30 , 357 –366 .
68.
Bale
C. W.
,
Chartrand
P.
,
Degterov
S. A.
,
Eriksson
G.
,
Hack
K.
,
Mahfoud
R. B.
,
Melançon
J.
,
Pelton
A. D.
and
Petersen
S.
CALPHAD , 2002 , 26 , 189 –228 .
69.
Davies
R. H.
,
Dinsdale
A. T.
,
Gisby
J. A.
J. A. J. Robinson and
70.
Martin
S. M.
: CALPHAD , 2002 , 26 , 229 –271 .
71.
Chen
S.-L.
,
Daniel
S.
,
Zhang
F.
,
Chang
Y. A.
,
Yan
X. -Y.
,
Xie
F.-Y.
,
Schmid-Fetzer
R.
and
Oates
W. A.
CALPHAD , 2002 , 26 , 175 –188 .
72.
Andersson
J.-O.
,
Helander
T.
,
H8glund
L.
,
Shi
P.
and
Sundman
B.
CALPHAD , 2002 , 26 , 273 –312 .
73.
Yokokawa
H.
,
Yamauchi
S.
and
Matsumoto
T.
CALPHAD , 2002 , 26 , 155 –166 .
74.
75.
Cheynet
B.
,
Chevalier
P.-Y.
and
Fischer
E.
CALPHAD , 2002 ,26 , 167 –174 .
76.Outotec HSC Chemistry: available at : www.outotec.com.
77.
Saunders
N.
,
Guo
Z.
,
Li
X.
,
Miodownik
A. P.
and
Schillé
J.-P.
JOM, 2003, 55, (12), 60 –65 .
78.
Kattner
U. R.
: J. Phase Equilib. Diffus ., 2006 , 27 , 126 –132 .
79.Thermotech Sente Software: available at : www.thermo-tech.co.uk/.
80.Scientific Group Thermodata Europe: available at : www.sgte.org
81.CompuTherm LLC: available at : www.computherm.com.
82.FactSage: available at : www.factsage.com
83.Materials Design Technology: available at : www.materials-design.co.jp/indexE.htm
84.
85.
86.Thermo-Calc Software: available at : www.thermocalc.com/
87.
Ansara
I.
,
Dinsdale
A. T.
and
Rand
M. H.
‘COST 507 — thermochemical database for light metal alloys’ , Vol. 2 ; 1998, Luxembourg, Office for Official Publications of the European Communities.
88.
Kroupa
A.
and
Vizdal
J.
Defect Diffus. Forum , 2007 , 263 , 99 –104 .
89.
Fick
A.
: Poggendorff's Annalen , 1855 , 94 , 59 –86 .
90.
Fick
A.
: Philos. Mag. A , 1855 , 10A , 30 –39 .
91.
Onsager
L.
: Phys. Rev ., 1931 , 37 , 405 –426 .
92.
Onsager
L.
: Phys . Re v ., 1931, 38, 2265-2279.
93.
Philibert
J.
: Diffus. Fundam ., 2006 , 4, 6 .1-6 .19 .
94.
Koiwa
M.
: Mater. Trans. JIM , 1998 , 39 , 1169 –1179 .
95.
Kizilyalli
M.
,
Corish
J.
and
Metselaar
R.
Pure Appl. Chem ., 1999 , 71 , 1307 –1325 .
96.
Philibert
J.
: ‘Atom movements: diffusion and mass transport in solids’ , 577 ; 1991 , Les Ulis , Editions de Physique .
97.
Shewmon
P.
: ‘Diffusion in Solids’, 2nd edn; 1989, Warrendale, PA, TMS.
98.
Kirkendall
E. O.
: Trans. AIME , 1942 , 147 , 104 –110 .
99.
Smigelskas
A. D.
and
Kirkendall
E. O.
Trans. AIME , 1947 , 171 ,130 –142 .
100.
Darken
L. S.
: Trans. AIME, 1948, 175, 184 –201 .
101.
Boltzmann
L.
: Ann. Phys ., 1894 , 53 , 959 –964 .
102.
Matano
C.
: Jpn J. Phys ., 1933 , 8 , 109 –113 .
103.
Sauer
V. F.
and
Friese
V.
Z. Elektrochem ., 1962 , 66 , 353 –363 .
104.
Wagner
C.
: Acta Metall, 1969, 17, 99 –107 .
105.
Dayananda
M. A.
: Metall Mater. Trans. A , 1996 , 27A , 2504 –2509 .
106.
Dayananda
M. A.
: MultiDiflux Purdue University, 2004, availableat: https://engineering.purdue.edu/MSE/Research/MultiDiFlux/index.htm.
107.
Janotti
A.
,
Krcmar
M.
,
Fu
C. L.
and
Reed
R. C.
Phys. Rev. Lett ., 2004 , 92 , 085901 .
108.
Krcmar
M.
,
Fu
C. L.
,
Janotti
A.
and
Reed
R. C.
Acta Mater., 2005, 53, 2369 –2376 .
109.
Mishin
Y.
and
Farkas
D.
Philos. Mag. A , 1997 , 75A , 187 –199 .
110.
Mishin
Y.
,
Lozovoi
A. Y.
and
Alavi
A.
Phys. Rev. B , 2003 , 67B , 014201 .
111.
Mishin
Y.
and
Herzig
C.
Acta Mater ., 2000 , 48 , 589 –623 .
112.
Mishin
Y.
,
Belova
I. V.
and
Murch
G. E.
Defect Diffus. Forum , 2005 , 237-240 , 271 –276 .
113.
Chamati
H.
,
Papanicolaou
N. I.
,
Mishin
Y.
and
Papaconstantopoulos
D. A.
Surf Sci ., 2006 , 600 , 1793 –1803 .
114.
van der Ven
A.
,
Ceder
G.
,
Asta
M.
and
Tepesch
P. D.
Phys. Rev. B, 2001, MB, 184307.
115.
Yu
H.-C.
,
Yeon
D.-H.
,
vander Ven
A.
and
Thornton
K.
Acta Mater ., 2007 , 55 , 6690 –6704 .
116.
Helander
T.
and
Agren
J.
Acta Mater ., 1999 , 47 , 3291 –3300 .
117.
Helander
T.
and
Agren
J.
Acta Mater ., 1999 , 47 , 1141 –1152 .
118.
Kucera
J.
and
Million
B.
Metall Trans ., 1970 , 1 , 2603 –2606 .
119.
Jönsson
B.
: Z. Metallkd , 1994 , 85 , 502 –509 .
120.
Jönsson
B.
: Z. Metallkd , 1992 , 83 , 349 –355 .
121.
Jönsson
B.
: Z. Metallkd , 1994 , 85 , 498 –501 .
122.
Braun
R.
and
Feller-Kniepmeier
M.
Scr. Metall , 1986 , 20 , 7 –11 .
123.J. &# O0C4;gren : Acta Metall , 1982 , 30 , 841 –851 .
124.J. &# O0C4;gren : ISIJ Int ., 1992 , 32 , 291 –296 .
125.
Girifalco
L. A.
: J. Phys. Chem. Solids , 1964 , 24 , 323 –333 .
126.
Tökei
Z.
,
Bernardini
J.
,
Gas
P.
and
Beke
D. L.
Acta Mater ., 1997 , 45 , 541 –546 .
127.
Campbell
C. E.
: Acta Mater ., 2008 , 56 , 4277 –4290 .
128.
Hallström
S.
,
Hoglund
L.
and
Agren
J.
Presentation at Proc. 6th Euro. Conf. on ‘Stainless steel’, Helsinki, Finland, June 2008, The Swedish Steel Producers’ Association.
129.Thermo-Calc: ‘Example i
2: Diffusion of carbon in cementite’, in ‘DICTRA Examples’, Version 24 edn; 2006, Stockholm, Sweden, Thermo-Calc AB.
130.
Hillert
M.
,
Hoglund
L.
and
Agren
J.
J. Appl. Phys ., 2005 , 98 , 053511 .
131.
Jansson
B.
: ‘Evaluation of parameters in thermochemical models using different types of experimental data simultaneously’, Report TRITA-MAC-0234, Royal Institute of Technology, Stockholm, Sweden, 1984.
132.
Borgenstam
A.
,
Engstr6m
A.
,
Hoglund
L.
and
Agren
J.
J. Phase Equilib ., 2000 , 21 , 269 –280 .
133.
Campbell
C. E.
,
Boetttinger
W. J.
and
Kattner
U. R.
Acta Mater ., 2002 , 50 , 775 –792 .
134.
Campbell
C. E.
: J. Phase Equilib. Diffus ., 2005 , 26 , 435 –440 .
135.
Hoglund
L.
: unpublished work, DICTRA Toolbox, Thermo-Calc AB, Stockholm, Sweden, 2004.
136.
Brown
A. M.
and
Ashby
M. F.
Acta Metall , 1980 , 28 , 1085-110
1 .
137.
Manning
J. R.
: Metall Trans ., 1970 , 1 , 499 –505 .
138.
Campbell
C. E.
,
Zhao
J.-C.
and
Henry
M. F.
J. Phase Equilib. Diffus ., 2004 , 25 , 6 –15 .
139.
Gómez-Acebo
T.
,
Navarcorena
B.
and
Castro
F.
J. Phase Equilib. Diffus ., 2004 , 25 , 237 –251 .
140.
Ma
X.
,
Toffolon-Masclet
C.
,
Guilbert
T.
,
Hamon
D.
,
Brachet
J. C.
J. Nucl. Mater ., 2008 , 377 , 359 –369 .
141.
He
Y. L.
,
Li
L.
,
Huang
S. G.
J. Vleugels and 0. van der Bies : Rare Met ., 2007 , 26 , 492 –497 .
142.
Haglund
S.
and
Agren
J.
Acta Mater ., 1998 , 46 , 2801 –2807 .
143.
Ghosh
G.
: Acta Mater ., 2001 , 49 , 2609 –2624 .
144.
Ghosh
G.
and
Liu
Z.-K.
J. Electron. Mater ., 1998 , 27 , 1362 –1366 .
145.
Larsson
H.
and
Agren
J.
Comput . Mater. Sc i ., 2005 , 34, 254 –263 .
146.
Strandlund
H.
and
Larsson
H.
Defect Diffus. Forum , 2004 , 233 , 97 –133 .
147.
Steinbach
I.
,
Bottger
B.
,
Eiken
J.
,
Warnken
N.
and
Fries
S. G.
J. Phase Equilib. Diffus ., 2007 , 28, 101 –106 .
148.
Wen
Y. H.
,
Wang
B.
,
Simmons
J. P.
and
Wang
Y.
Acta Mater ., 2006 , 54 , 2087 –2099 .
149.
Wu
K.
,
Chang
Y. A.
and
Wang
Y.
Scr. Mater ., 2004 , 50 , 1145 –1150 .
150.
Simmons
J. P.
,
Wen
Y.
,
Shen
C.
and
Wang
Y. Z.
Mater. Sci. Eng. A , 2004 , A365 , 136 –143 .
151.
Cha
P.-R.
,
Yeon
D.-H.
and
Yoon
J.-K.
Acta Mater ., 2001 , 49 , 3295 –3307 .
152.
Chen
Q.
,
Ma
N.
,
Wu
K. S.
and
Wang
Y. Z.
Scr. Mater ., 2004 , 50 , 471 –476 .
153.
Asp
K.
and
Agren
J.
Acta Mater ., 2006 , 54 , 1241 –1248 .
154.
Brockman
W. B.
and
Morral
J. E.
‘Profiler: diffusion couple software to predict concentration profiles’: 1993, Storrs, CT, University of Connecticut.
155.
Thompson
M. S.
and
Morral
J. E.
Acta Metall ., 1986 , 34 ,339 –346 .
156.
Kattner
U. R.
,
Eriksson
G.
,
Hahn
I.
,
Schmid-Fetzer
R.
,
Sundman
B.
,
Swamy
V.
,
Kussmaul
A.
,
Spencer
P. J.
,
Anderson
T. J.
,
Chart
T. G.
,
Costae Silva
A.
,
Jansson
B.
,
Lee
B.-J.
and
Schalin
M.
CALPHAD , 2000 , 24 , 55 –94 .
157.
�C4;gren
J.
,
Hayes
F. H.
,
Hoglund
L.
,
Kattner
U. R.
,
Legendre
B.
and
Schmid-Fetzer
R.
:
Metallkd
Z.
2002 , 93 , 128 –142 .
158.
Kaufman
L.
(ed.): ‘User applications of alloy phase diagrams’; 1987, Metals Park, OH, ASM International.
159.
Hayes
F. H.
(ed.): ‘User aspects of phase diagrams’; 1991, London, The Institute of Metals.
160.
Hack
K.
(ed.): ‘The SGTE casebook, thermodynamics at work’; 1996, London, The Institute of Metals.
161.
Moon
K.-W.
,
Boettinger
W. J.
,
Kattner
U. R.
,
Handwerker
C. A.
and
Lee
D.-J.
J. Electron. Mater ., 2001 , 30 , 45 –52 .
162.
Yoon
S. W.
and
Lee
H. M.
CALPHAD , 1998 , 22 , 167 –178 .
163.
Boettinger
W. J.
and
Kattner
U. R.
Metall. Mater. Trans. A , 2002 , 33A , 1779 –1794 .
164.
Liu
H. S.
,
Liu
C. L.
,
Ishida
K.
and
Jin
Z. P.
J. Electron. Mater ., 2003 , 32 , 1290 –1296 .
165.
Boettinger
W. J.
,
Kattner
U. R.
,
Moon
K.-W.
and
Perepezko
J. H.
in ‘Methods for phase diagram determination’, (ed. J.-C. Zhao), 151-221; 2007, Amsterdam, Elsevier.
166.
Tanaka
T.
,
Hack
K.
and
Hara
S.
MRS Bull ., 1999 ,24 , (4 ), 45 –50 .
167.
Pajarre
R.
,
Koukkari
P.
,
Tanaka
T.
and
Lee
J.
CALPHAD , 2006 , 30 , 196 –200 .
168.
Banerjee
D. K.
,
Samonds
M. T.
,
Kattner
U. R.
and
Boettinger
W. J.
in ‘Solidification processing 1997’, (ed.
Beech
J.
and
Jones
H.
354-357; 1997, Sheffield, University of Sheffield.
169.
Schneider
M. C.
,
Gu
J. P.
,
Beckermann
C.
,
Boettinger
W. J.
and
Kattner
U. R.
Metall. Mater. Trans. A , 1997 , 28A , 1517 –1531 .
170.
Campbell
C. E.
,
Boettinger
W. J.
,
Hansen
T.
,
Merewether
P.
and
Mueller
B. A.
in ‘Complex inorganic solids: structural, stability and magnetic properties of alloys’, 241-249; 2005, New York, Springer.
171.
Saunders
N.
: in ‘Superalloys 1996’, 101-110; 1996, Warrendale, PA, TMS.
172.
Hoglund
L.
and
Agren
J.
Acta Mater ., 2001 , 49 , 1311 –1317 .
173.
Campbell
C. E.
and
Boettinger
W. J.
Metall. Mater. Trans. A , 2000 , 31A , 2835 –2847 .
174.
Frykholm
R.
,
Ekroth
M.
,
Jansson
B.
J. Agren and H.-0. Andren : Acta Mater ., 2003 , 51 , 1115 –1121 .
175.
Larsson
H.
,
Strandlund
H.
and
Hillert
M.
Acta Mater ., 2006 , 54 , 945 –951 .
176.
Strandlund
H.
and
Larsson
H.
Metall. Mater. Trans. A , 2006 , 37A , 1785 –1789 .
177.
Larsson
H.
and
Engstrom
A.
Acta Mater ., 2006 , 54 , 2431 –2439 .
178.
Wiener
O.
: Abh. Math. — Phys. Kön. Sachs. Ges. Wis., 1912, 32, 509.
179.
Hashin
Z.
and
Shtrikman
S.
J. AppL Phys ., 1962 , 33 , 3125 .
180.
Dahl
K. V.
,
Hald
J.
and
Horsewell
A.
Defect Diffus. Forum , 2006 , 258-260 , 73 –78 .
181.
Jou
H. J.
,
Voorhees
P.
and
Olson
G. B.
in ‘Superalloys 2004’, 877-886; 2004, Warrendale, PA, TMS.
182.
Olson
G. B.
,
Jou
H. J.
,
Jung
J-W.
and
Sebastian
J. T.
Superalloys 2008, 923-932; 2008, Warrendale, PA, TMS.
183.
Strandlund
H.
,
Lu
X.
,
Chen
Q.
and
Engstrom
A.
Proc. Int. Conf. on ‘Materials science and technology’, 38; 2007, Detroit, MI, American Ceramic Society.
184.
Wu
K.
: Proc. Int. Conf. on ‘Materials science and technology’, Detroit, MI, 51; 2007, American Ceramic Society.
185.
Lu
X.-G.
,
Selleby
M.
and
Sundman
B.
CALPHAD , 2005 , 29 , 68 –89 .
186.
Ghosh
G.
and
Olson
G. B.
Acta Mater ., 2007 , 55 , 3281 –3303 .
187.
Saha
A.
and
Olson
G. B.
J. Comput. Aided Mater. Design , 2007 , 14 , 177 –200 .
188.
Campbell
C. E.
and
Olson
G. B.
J. Comput. Aided Mater. Design , 2000 , 7 , 145 –170 .
189.
Ghosh
G.
and
Olson
G. B.
J. Phase Equilib ., 2001 , 22 , 199 –207 .
190.
Ghosh
G.
and
Olson
G. B.
Acta Mater ., 2002 , 50 , 2099 –2119 .
191.
Olson
G. B.
: Science , 1997 , 277 , 1237 –1242 .
192.
Liu
Z. K.
,
Chen
L. Q.
,
Raghavan
P.
,
Du
Q.
,
Sofo
J. O.
,
Langer
S. A.
and
Wolverton
C.
J. Comput. Aided Mater. Design , 2004 , 11 , 183 –199 .
193.
Allison
J.
,
Li
M.
,
Wolverton
C.
and
Su
X.
JOM , 2006 , 48 , (11 ), 28 –35 .
194.
McDowell
D. L.
: JOM , 2007 , 49 , (9 ), 21 –25 .
195.
Kuehmann
C. J.
and
Olson
G. B.
Mater. Sci. TechnoL , 2009 , 25 , 472 –478 .