The present work incorporates a modified Q-state Monte Carlo (Potts) model to evaluate two-dimensional annealing of representative paramagnetic and diamagnetic polycrystalline materials in the presence of a magnetic field. Anisotropies in grain boundary energy, caused by differences in grain orientation (texturing), and the presence of an external magnetic field are examined in detail. In the former case, the Read–Shockley equations are used, in which grain boundary energies are computed using a low-angle misorientation approximation. In the latter case, magnetic anisotropy is simulated based on the relative orientation between the principal grain axis and the external magnetic field vector. Among other findings, the results of texture development subject to a magnetic field showed an increasing orientation distribution function (ODF) asymmetry over time, with higher intensities favoring the grains with principal axes most closely aligned with the magnetic field direction. The magnetic field also tended to increase the average grain size, which was accompanied by a corresponding decrease in the total grain boundary energy.

References

References
1.
Tjong
,
S. C.
, and
Chen
,
H.
,
2004
, “
Nanocrystalline Materials and Coatings
,”
Mater. Sci. Eng. R
,
45
(1–2), pp.
1
88
.
2.
Liu
,
Z. J.
,
Zhang
,
C. H.
,
Shen
,
Y. G.
, and
Mai
,
Y.-W.
,
2004
, “
Monte Carlo Simulation of Nanocrystalline TiN/Amorphous SiNx Composite Films
,”
J. Appl. Phys.
,
95
(
2
), pp.
758
760
.
3.
Lu
,
C.
,
Mai
,
Y.-W.
, and
Shen
,
Y. G.
,
2006
, “
Recent Advances on Understanding the Origin of Superhardness in Nanocomposite Coatings: A Critical Review
,”
J. Mater. Sci.
,
41
(
3
), pp.
937
950
.
4.
Yang
,
W.
,
Chen
,
L.
, and
Messing
,
G.
,
1995
, “
Computer Simulation of Anisotropic Grain Growth
,”
Mater. Sci. Eng. A
,
195
(
1–2
), pp.
179
187
.
5.
de Rango
,
P.
,
Lees
,
M.
,
Lejay
,
P.
,
Sulpice
,
A.
,
Tournier
,
R.
,
Ingold
,
M.
,
Germi
,
P.
, and
Pernet
,
M.
,
1991
, “
Texturing of Magnetic Materials at High Temperature by Solidification in a Magnetic Field
,”
Nature
,
349
(
6312
), pp.
770
772
.
6.
Li
,
X.
,
Ren
,
Z. M.
, and
Fautrelle
,
Y.
,
2006
, “
Effect of a High Axial Magnetic Field on the Microstructure in a Directionally Solidified Al–Al2Cu Eutectic Alloy
,”
Acta Mater.
,
54
(
20
), pp.
5349
5360
.
7.
Deng
,
P. R.
,
Li
,
J. G.
, and
Xu
,
Z. M.
,
2006
, “
Texture Evolution of Terfenaol-D by Solidification in a Magnetic Field
,”
J. Appl. Phys.
,
100
(
5
), p.
053905
.
8.
Mullins
,
W. W.
,
1956
, “
Magnetically Induced Grain-Boundary Motion in Bismuth
,”
Acta Metall.
,
4
(
4
), pp.
421
432
.
9.
Molodov
,
D. A.
,
Gottstein
,
G.
,
Heringhaus
,
F.
, and
Shvindlerman
,
L. S.
,
1997
, “
Motion of Planar Grain-Boundaries in Bismuth-Bicrystals Driven by a Magnetic Field
,”
Scr. Mater.
,
37
(
8
), pp.
1207
1213
.
10.
Sheikh-Ali
,
A. D.
,
Molodov
,
D. A.
, and
Garmestani
,
H.
,
2002
, “
Magnetically Induced Texture Development in Zinc Alloy Sheet
,”
Scr. Mater.
,
46
(
12
), pp.
857
862
.
11.
Sheikh-Ali
,
A.
,
Molodov
,
D. A.
, and
Garmestani
,
H.
,
2003
, “
Boundary Migration in Zn Bicrystal Induced by a High Magnetic Field
,”
Appl. Phys. Lett.
,
82
(
18
), pp.
3005
3007
.
12.
Molodov
,
D. A.
,
Bollmann
,
C. B.
,
Konijnenberg
,
P. J.
,
Barrales-Mora
,
L. A.
, and
Mohles
,
V.
,
2007
, “
Annealing Texture and Microstructure Evolution in Titanium During Grain Growth in an External Magnetic Field
,”
Mater. Trans.
,
48
(
11
), pp.
2800
2808
.
13.
Barrales-Mora
,
L. A.
,
Mohles
,
V.
,
Konijnenberg
,
P. J.
, and
Molodov
,
D. A.
,
2007
, “
A Novel Implementation for the Simulation of 2-D Grain Growth With Consideration to External Energetic Fields
,”
Comput. Mater. Sci.
,
39
(
1
), pp.
160
165
.
14.
Lei
,
H. C.
,
Zhu
,
X. B.
,
Sun
,
Y. P.
,
Hu
,
L.
, and
Song
,
W. H.
,
2009
, “
Effects of Magnetic Field on Grain Growth of Non-Ferromagnetic Metals: A Monte Carlo Simulation
,”
EPL
,
85
(
3
), p.
38004
.
15.
Kocks
,
U. F.
,
Tome
,
C. N.
,
Wenk
,
H. R.
, and
Mecking
,
H.
,
1998
,
Texture and Anisotropy: Preferred Orientations in Polycrystals and Their Effect on Materials Properties
,
Cambridge University Press
,
Cambridge, UK
.
16.
Roe
,
R. J.
,
1965
, “
Description of Crystallite Orientation in Polycrystalline General Solution to Pole Figure Inversion
,”
J. Appl. Phys.
,
36
(
6
), pp.
2024
2031
.
17.
Holm
,
E. A.
,
Hassold
,
G. N.
, and
Miodownik
,
M. A.
,
2001
, “
On Misorientation Distribution Evolution During Anisotropic Grain Growth
,”
Acta Mater.
,
49
(
15
), pp.
2981
2991
.
18.
Srolovitz
,
D. J.
,
Anderson
,
M. P.
,
Grest
,
G. S.
, and
Rollett
,
A. D.
,
1988
, “
Computer Simulation of Recrystallization—II. Heterogeneous Nucleation and Growth
,”
Acta Metall.
,
36
(
8
), pp.
2115
2128
.
19.
Allen
,
J. B.
,
Cornwell
,
C. F.
,
Devine
,
B. D.
, and
Welch
,
C. R.
,
2013
, “
Simulations of Anisotropic Grain Growth in Single Phase Materials Using Q-State Monte Carlo
,”
Comput. Mater. Sci.
,
71
, pp.
25
32
.
20.
Anderson
,
M. P.
,
Srolovitz
,
D. J.
,
Grest
,
G. S.
, and
Sahni
,
P. S.
,
1984
, “
Computer Simulation of Grain Growth—I. Kinetics
,”
Acta Metall.
,
32
(
5
), pp.
783
792
.
21.
Metropolis
,
N.
,
Rosenbluth
,
A. W.
,
Rosenbluth
,
M. N.
,
Teller
,
A. T.
, and
Teller
,
E. J.
,
1953
, “
Equation of State Calculations by Fast Computing Machines
,”
J. Chem. Phys.
,
21
(
6
), pp.
1087
1092
.
22.
Garcia
,
A. L.
,
Tikare
,
V.
, and
Holm
,
E. A.
,
2008
, “
Three-Dimensional Simulation of Grain Growth in a Thermal Gradient With Non-Uniform Grain Boundary Mobility
,”
Scr. Mater.
,
59
(
6
), pp.
661
664
.
23.
Atkinson
,
H. V.
,
1988
, “
Theories of Normal Grain Growth in Pure Single Phase Systems
,”
Acta Metall.
,
36
(
3
), pp.
469
491
.
24.
Frank
,
F. C.
,
1988
, “
Orientation Mapping
,”
Metall. Trans. A
,
19
(
3
), pp.
403
408
.
You do not currently have access to this content.