Linking phase-field model to CALPHAD: application
to precipitate shape evolution in Ni-base alloys
J.Z. Zhu*, Z.K. Liu, V. Vaithyanathan, L.Q. Chen
Department of Materials Science and Engineering, The Pennsylvania State University, 119 Steidle Building, University Park,
PA 16802-5005, USA
Received 9 October 2001; accepted 5 December 2001
A three-dimensional phase-field model is proposed with the thermodynamic and kinetic parameters directly ex-
tracted from existing databases using the CALPHAD method. We modelled the c0precipitate microstructure evolution
in a Ni-base alloy, particularly a single precipitate morphology at different sizes using independently assessed ther-
modynamic, kinetic and structural parameters. ? 2002 Published by Elsevier Science Ltd. on behalf of Acta Materialia
Keywords: Phase field; CALPHAD; Ni-base alloys; Microstructure; Computer simulation
The phase-field approach has found increasing
applications in modelling phase transformation
and microstructural evolution in solids . One of
its main advantages is that the temporal evolution
of any arbitrary microstructures can be predicted
without any a priori assumptions about their evo-
lution path. For example, it has been used to ex-
plain many of the morphological evolutions in
coherent solids including Ni-base superalloys [2–5].
Despite the tremendous success of phase-field
modelling in predicting many of the experimen-
tally observed microstructures in solids, additional
progress is required in order to apply it to predict
the microstructure evolution in real multi-compo-
nent alloy systems. For example, there exists no
systematic approach for obtaining the thermody-
namic and kinetic input to the phase-field models
although a number of efforts have been reported in
connecting phase-field models with existing ther-
modynamic and kinetic databases. Furthermore,
the dependence of kinetic parameters such as dif-
fusional mobility of atoms and of mechanical
properties such as elastic constants on the compo-
sition is generally ignored whereas in real systems
they are almost always composition dependent.
Finally, existing phase-field simulations have been
largely confined to two-dimension and the exten-
sion to three-dimensional (3D) systems requires
efficient numerical algorithms.
The main purpose of this paper is to describe our
initial attempt to develop a 3D phase-field model
for modelling the microstructure evolution in Ni-
basesuperalloys. The localfree energyasafunction
Scripta Materialia 46 (2002) 401–406
*Corresponding author. Tel.: +1-814-8650389; fax: +1-814-
E-mail address: firstname.lastname@example.org (J.Z. Zhu).
1359-6462/02/$ - see front matter ? 2002 Published by Elsevier Science Ltd. on behalf of Acta Materialia Inc.
particles and plates or undergoing splitting to form
doublets or octets, which should occur only when
the particle size grows to a very large length scale.
In summary, we have developed a 3D phase-
field model to link with CALPHAD method
through the local free energy construction as a
function of field variables where most important
thermodynamic and kinetic parameters are taken
from either a database or independent experimen-
tal measurements. The compositional dependence
of atomic mobilities and elastic constants is taken
into account in solving the phase-field equations
and elastic equilibrium equations. The Ni3Al pre-
cipitate shape evolution in a disordered fcc matrix,
as illustrated from the simulations, depends on the
balance between the interfacial energy and the
elastic energy relaxation. Carrying out 3D simu-
lations in a larger system size is currently underway
to have a complete analysis of the precipitate
coarsening behavior in Ni-base superalloys.
The authors are grateful for financial support
from NASA under grant no. NCC3-920 and from
the National Science Foundation under grant nos.
DMR-0122638 and DMR-9983532. The simula-
tion was performed at the San Diego Supercom-
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