The system of governing equations was developed in order to descibe the transformation of multiple crystals for the case of rapid solidification. The model represents itself the extention of a phase field model of multi–grain crystallization by Moelans et.al. The traveling wave solution of phase field model were developed and the description of the dynamics of the moving interface is analysed.

1.
L.
Granasy
,
T.
Pusztai
,
J. A.
Warren
,
Journal of Physics: Condensed Matter
16
(
41
),
R1205
35
(
2004
).
2.
R.
Folch
,
M.
Plapp
,
Phys. Rev. E
72
,
011602
011627
(
2005
).
3.
D.A.
Cogswell
,
W.C.
Carter
,
Phys. Rev. E
83
,
061602
1–13
(
2011
).
4.
I.
Steinbach
,
L.
Zhang
,
M.
Plapp
,
Acta Materialia
,
60
,
2689
2701
(
2012
).
5.
L.
Zhang
,
I.
Steinbach
,
Acta Materialia
60
,
2702
2710
(
2012
).
6.
D.
Fan
,
L.-Q.
Chen
,
Acta Materialia
45
(
2
),
611
622
(
1997
).
7.
N.
Moelans
,
B.
Blanpain
,
P.
Wollants
,
Phys. Rev. B
78
,
024113
1–13
(
2008
).
8.
N.
Moelans
,
B.
Blanpain
,
P.
Wollants
,
Phys. Rev. Lett.
101
,
025502
(
2008
).
9.
N.
Moelans
,
Acta Materialia
,
59
,
1077
1086
(
2011
).
10.
Y.
Fu
,
J.
Michopoulos
,
B.
Gnanasekaran
,
Comput. Mater. Sci.
155
,
457
465
(
2018
).
11.
P.
Galenko
,
D.
Jou
,
Phys. Rev. E
71
,
046125
1–13
(
2005
).
12.
D. A.
Danilov
,
V. G.
Lebedev
,
P. K.
Galenko
,
J. Non-Equilibrium Therm.
39
(
2
),
93
111
(
2014
).
13.
P. K.
Galenko
,
I. G.
Nizovtseva
,
N.
Moelans
, “
Phase-field model derivation for computer simulation of rapid crystal growth in polycrystalline alloys
”,
Math. and Comp. Simulations
(in press).
14.
H.
Ravash
,
J.
Vleugels
,
N.
Moelans
,
J. Materials Science
52
,
13852
13867
(
2017
).
15.
A.
Salhoumi
,
P.
Galenko
,
Physica A
447
,
161
171
(
2016
).
16.
I. G.
Nizovtseva
,
P. K.
Galenko
,
D. V.
Alexandrov
,
J. Phys. A: Math. Theor.
49
,
435201
1–14
(
2016
).
17.
I. G.
Nizovtseva
,
P. K.
Galenko
,
Phil. Trans. R. Soc. A
376
,
20170202
1–15
(
2018
).
18.
H.
Jones
,
Rep. Prog. Phys.
36
,
1425
1497
(
1973
).
19.
D. V.
Alexandrov
,
A. Yu.
Zubarev
,
Phil. Trans. R. Soc. A
377
,
20180353
1–9
(
2019
).
20.
A. A.
Ivanov
,
I. V.
Alexandrova
,
D. V.
Alexandrov
,
Phil. Trans. R. Soc. A
377
,
20180215
1–11
(
2019
).
21.
E. V.
Makoveeva
,
D. V.
Alexandrov
,
Phil. Trans. R. Soc. A
377
,
20180210
1–10
(
2019
).
22.
D. V.
Alexandrov
,
I. V.
Alexandrova
,
Phil. Trans. R. Soc. A
377
,
20180209
1–10
(
2019
).
23.
D. V.
Alexandrov
,
I. A.
Bashkirtseva
,
L. B.
Ryashko
,
Phil. Trans. R. Soc. A
376
,
20170216
1–9
(
2018
).
24.
D.V.
Alexandrov
,
A.A.
Ivanov
,
I.V.
Alexandrova
,
Phil. Trans. R. Soc. A
376
,
20170217
1–10
(
2018
).
25.
E.V.
Makoveeva
,
D.V.
Alexandrov
,
Phil. Trans. R. Soc. A
376
,
20170327
1–12
(
2018
).
This content is only available via PDF.
You do not currently have access to this content.