Grain growth is a broad field of study that covers several scientifically and technically interesting characteristics. Normal grain growth kinetics and its associated parabolic growth law and self-similar size distributions, grain boundary pinning, abnormal grain growth, the effect of triple junctions and quadruple points as well as grain growth in thin films are the most important current topics of grain growth research. In this critical assessment of grain growth in metals, we present and discuss some of the most important unresolved issues that have been a subject of research for many years.
HillertM.On the theory of normal and abnormal grain growth. Acta Metall. 1965;13:227–238. doi: 10.1016/0001-6160(65)90200-2
4.
AtkinsonHV.Overview no. 65. Theories of normal grain growth in pure single phase systems. Acta Metall. 1988;36:469–491. doi: 10.1016/0001-6160(88)90079-X
5.
RiosPR.Overview no. 62. A theory for grain boundary pinning by particles. Acta Metall. 1987;35:2805–2814. doi: 10.1016/0001-6160(87)90280-X
6.
FayadW, ThompsonCV, FrostHJ.Steady-state grain-size distributions resulting from grain growth in two dimensions. Scripta Mater. 1999;40:1199–1204. doi: 10.1016/S1359-6462(99)00034-2
7.
RiosPR, DalpianTG, BrandãoVS, Comparison of analytical grain size distributions with three-dimensional computer simulations and experimental data. Scripta Mater. 2006;54:1633–1637. doi: 10.1016/j.scriptamat.2006.01.007
8.
FuchizakiK, KusabaT, KawasakiK.Computer modelling of three-dimensional cellular pattern growth. Phil Mag. B. 1995;71:333–357. doi: 10.1080/13642819508239038
9.
WeygandD, BrechetY, LepinouxJ, Three-dimensional grain growth: a vertex dynamics simulation. Phil Mag. B. 1999;79:703–716. doi: 10.1080/13642819908205744
MiessenC, Barrales-MoraLA, ShvindlermanLS, An advanced level set approach to grain growth – accounting for grain boundary anisotropy and finite triple junction mobility. Acta Mater. 2015;99:39–48. doi: 10.1016/j.actamat.2015.07.040
12.
WakaiF, EnomotoN, OgawaH.Three-dimensional microstructural evolution in ideal grain growth general statistics. Acta Mater. 2000;48:1297–1311. doi: 10.1016/S1359-6454(99)00405-X
13.
BrakkeK.The motion of a surface by its mean curvature. Princeton ( NJ): Princeton University Press; 1977.
14.
KrillCEIII, ChenLQ.Computer simulation of 3-D grain growth using a phase-field model. Acta Mater. 2002;50:3057-3073.
15.
AndersonMP, GrestGS, SrolovitzDJ.Computer simulation of normal grain growth in three dimensions. Phil Mag. B. 1989;59:293–329. doi: 10.1080/13642818908220181
16.
ZöllnerD.A Potts model for junction limited grain growth. Comput Mater Sci. 2011;50:2712–2719. doi: 10.1016/j.commatsci.2011.04.024
17.
ZöllnerD.A new point of view to determine the simulation temperature for the Potts model simulation of grain growth. Comput Mater Sci. 2014;86:99–107. doi: 10.1016/j.commatsci.2014.01.044
18.
RowenhorstDJ, LewisAC, SpanosG.Three-dimensional analysis of grain topology and interface curvature in a β-titanium alloy. Acta Mater. 2010;58:5511–5519. doi: 10.1016/j.actamat.2010.06.030
19.
ZhangC, SuzukiA, IshimaruT, Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning. Metall Mater Trans. A. 2004;35A:1927–1933. doi: 10.1007/s11661-004-0141-5
20.
JensenDJ, LauridsenEM, MarguliesL, X-ray microscopy in four dimensions. Mater Today. 2006;9:18–25. doi: 10.1016/S1369-7021(05)71334-1
21.
BaruchelJ, BuffiereJY, CloetensP, Advances in synchrotron radiation microtomography. Scripta Mater. 2006;55:41–46. doi: 10.1016/j.scriptamat.2006.02.012
22.
BaruchelJ, BleuetP, BravinA, Advances in synchrotron hard X-ray based imaging. C R Phys. 2008;9:624–641. doi: 10.1016/j.crhy.2007.08.003
23.
GlicksmanME.Analysis of 3-D network structures. Phil Mag. 1985;52:3–31.
RiosPR, GlicksmanME.Topological and metrical analysis of normal grain growth in three dimensions. Acta Mater. 2007;55:1565–1571. doi: 10.1016/j.actamat.2006.10.017
26.
RiosPR, GlicksmanME.Modeling polycrystals with regular polyhedra. Mater Res. 2007;9:231–236. doi: 10.1590/S1516-14392006000200021
27.
RiosPR, GlicksmanME, LewisDJ.Regular N-hedra: A topological approach for analyzing three-dimensional textured polycrystals. Acta Mater. 2007;55:4167–4180. doi: 10.1016/j.actamat.2007.03.014
28.
ZöllnerD, DakeJ, KrillCE.Simulation der Korngrenzenmigration in polykristallinem Graphen G. Petzow, Fortschritte in der Metallographie, Sonderband 45, DGM INVENTUM;2013, p. 247–10.
29.
ZöllnerD, StreitenbergerP.Three-dimensional normal grain growth: Monte Carlo Potts model simulation and analytical mean field theory. Scripta Mater. 2006;54:1697–1702. doi: 10.1016/j.scriptamat.2005.12.042
30.
StreitenbergerP, ZöllnerD.Effective growth law from three-dimensional grain growth simulations and new analytical grain size distribution. Scripta Mater. 2006;55:461–464. doi: 10.1016/j.scriptamat.2006.05.009
31.
ZöllnerD.Grain growth. In: Saleem Hashmi (editor-in-chief), Reference Module in Materials Science and Materials Engineering. Oxford: Elsevier;2016, p. 1–10.
32.
ZöllnerD, StreitenbergerP.Grain size distributions in normal grain growth. Prakt Metallogr. 2010;47:262–283. doi: 10.3139/147.110038
33.
ZöllnerD, StreitenbergerP.Serial sectioning of grain microstructures under junction control: an old problem in a new guise. IOP Conference Series: Mater Sci Eng.2015;82, 012080.
34.
AboavDA.The arrangement of grains in a polycrystal. Metallography. 1970;3:383–390. doi: 10.1016/0026-0800(70)90038-8
35.
ZöllnerD.On the Aboav–Weaire-law for junction limited grain growth in two dimensions. Comput Mater Sci. 2013;79:759–762. doi: 10.1016/j.commatsci.2013.07.031
36.
ZöllnerD, StreitenbergerP, RiosPR.Shedding some light on the early grain growth regime: about the effect of the initial microstructure on normal grain growth. Comput Mater Sci. 2016;113:11–20. doi: 10.1016/j.commatsci.2015.11.022
37.
LifshitzIM, SlyozovVV.The kinetics of precipitation from supersaturated solid solutions. J Phys Chem Sol. 1961;19:5–50. doi: 10.1016/0022-3697(61)90054-3
38.
WagnerC.Theorie der Alterung von Niederschliigen durch Umlosen. Z Elektrochem. 1961;65:581–591.
39.
PandeCS, McFaddenGB.Self-similar grain size distribution in three dimensions: a stochastic treatment. Acta Mater. 2010;58:1037–1044. doi: 10.1016/j.actamat.2009.10.020
40.
FischerFD, SvobodaJ, FratzlP.A thermodynamic approach to grain growth and coarsening. Phil Mag. B. 2003;83:1075–1093. doi: 10.1080/0141861031000068966
41.
StreitenbergerP, ZöllnerD.The envelope of size distributions in Ostwald ripening and grain growth. Acta Mater. 2015;88:334–345. doi: 10.1016/j.actamat.2015.01.035
42.
StreitenbergerP, ZöllnerD.Self-similar coarsening and the envelope theorem. Acta Mater. 2016;111:210–219. doi: 10.1016/j.actamat.2016.03.062
43.
RiosPR, GlicksmanME.Polyhedral model for self-similar grain growth. Acta Mater. 2008;56:1165–1171. doi: 10.1016/j.actamat.2007.11.010
MacPhersonRD, SrolovitzDJ.The von Neumann relation generalized to coarsening of three-dimensional microstructures. Nature. 2007;446:1053–1055. doi: 10.1038/nature05745
46.
GlicksmanME, RiosPR, LewisDJ.Mean width and caliper characteristics of network polyhedra. Phil Mag. 2009;89:389–403. doi: 10.1080/14786430802651513
47.
StreitenbergerP, ZöllnerD.Triple junction controlled grain growth in two-dimensional polycrystals and thin films: self-similar growth laws and grain size distributions. Acta Mater. 2014;78:114–124. doi: 10.1016/j.actamat.2014.06.022
48.
RivierN.Statistical crystallography structure of random cellular networks. Phil Mag. B. 1985;52:795–819. doi: 10.1080/13642818508240637
RiosPR.Irreversible thermodynamics, parabolic law and self-similar state in grain growth. Acta Mater. 2004;52:249–256. doi: 10.1016/j.actamat.2003.09.010
51.
ZilnykKD, LeiteGS, SandimHRZ, Grain growth inhibition by connected porosity in sintered niobium. Acta Mater. 2013;61:5821–5828. doi: 10.1016/j.actamat.2013.06.027
52.
LiuY, PattersonBR.Pore inhibited grain growth. Acta Metall Mater. 1993;41:2551–2656.
53.
RiosPR, GottsteinG, ShvindlermanLS.An irreversible thermodynamic approach to normal grain growth with a pinning force. Mater Sci Eng. A. 2002;332:231–235. doi: 10.1016/S0921-5093(01)01745-2
54.
SmithCS.Introduction to grains, phases, and interfaces – an interpretation of microstructure. Trans. AIME. 1948;175:15–51.
55.
RiosPR.Fonseca GS grain boundary pinning by Al6Mn precipitates in an Al-1wt%Mn alloy. Scripta Mater.2004;50:71–75. doi: 10.1016/j.scriptamat.2003.09.031
56.
RiosPR, FonsecaGS.Grain boundary curvature and particle pinning in an Al-1mass%Mn alloy. Scripta Mater. 2004;50:1373–1377. doi: 10.1016/j.scriptamat.2004.02.041
57.
ManoharPA, FerryM, ChandraT.Five decades of the Zener equation. ISIJ Int. 1998;38:913–924. doi: 10.2355/isijinternational.38.913
58.
RiosPR, FonsecaGS.Grain boundary pinning by particles. Mater Sci Forum. 2010;638-642:3907–3912.
59.
RiosPR, GlicksmanME.Topological theory of abnormal grain growth. Acta Mater. 2006;55:5313–5321. doi: 10.1016/j.actamat.2006.07.010
60.
RiosPR.Some theoretical considerations on abnormal grain growth. Mater Sci Forum. 1996;247-256:247–256.
61.
ThompsonCV, FrostHJ, SpaepenF.The relative rates of secondary and normal grain growth. Acta Metall. 1987;35:887–890. doi: 10.1016/0001-6160(87)90166-0
62.
RiosPR.Abnormal grain growth in pure materials. Acta Metall. 1992;40:2765–2768. doi: 10.1016/0956-7151(92)90346-G
63.
RiosPR.Abnormal growth in the presence of coarsening particles. Acta Metall. 1992;40:649–651. doi: 10.1016/0956-7151(92)90005-Y
64.
RiosPR.Abnormal grain growth in materials containing particles. Acta Metall. 1994;42:839–843. doi: 10.1016/0956-7151(94)90278-X
65.
KronbergML, WilsonFH.Secondary recrystallization in copper. Trans. AIME. 1949;185:501–514.
66.
JungS-H, YoonDY, KangS-JL.Mechanism of abnormal grain growth in ultrafine-grained nickel. Acta Mater. 2013;61:5685–5693. doi: 10.1016/j.actamat.2013.06.010
67.
BrunoJC, RiosPR.The grain size distribution and the detection of abnormal grain growth of austenite in an eutectoid steel containing niobium. Scripta Metall Mater. 1995;32:601–606. doi: 10.1016/0956-716X(95)90844-A
68.
RiosPR, GottsteinG.Texture evolution during normal and abnormal grain growth in an Al-1 wt% Mn alloy. Acta Mater. 2001;49:2511–2518. doi: 10.1016/S1359-6454(01)00143-4
69.
GladmanT.On the theory of the effect of precipitate particles on grain growth in metals. Proc R Soc Lond. A. 1966;294:298–309. doi: 10.1098/rspa.1966.0208
70.
RiosPR.Abnormal grain growth development from uniform grain size distributions. Acta Mater. 1997;45:1785–1789. doi: 10.1016/S1359-6454(96)00284-4
71.
FonsecaGS.O Estudo do Crescimento de Grão em uma liga Al-1%massa Mn[Study of grain growth in a Al-1mass%Mn alloy] [Ph.D. Thesis]. Brazil: Universidade Federal Fluminense, Volta Redonda;2007.
72.
GüntherK, AbbruzzeseG, FortunatiS, Recent technology developments in the production of grain-oriented electrical steel. Steel Res Int. 2005;76:413–421. doi: 10.1002/srin.200506030
MalowTR, KochCC.Grain growth in nanocrystalline iron prepared by mechanical attrition. Acta Mater. 1997;45:2177–2186. doi: 10.1016/S1359-6454(96)00300-X
75.
StreitenbergerP, ZöllnerD.Evolution equations and size distributions in nanocrystalline grain growth. Acta Mater. 2011;59:4235–4243. doi: 10.1016/j.actamat.2011.03.048
76.
ZöllnerD, StreitenbergerP.Studying the influence of triple junction energy and mobility on annealing processes. IOP Conference Series: Mater Sci Eng. 2015;89, 012061.
77.
ZöllnerD.Grain microstructure evolution in two-dimensional polycrystals under limited junction mobility. Scripta Mater. 2012;67:41–44. doi: 10.1016/j.scriptamat.2012.03.016
78.
ZöllnerD.Topology of grain microstructures in two dimensions: A comparison of grain boundary and triple junction controlled grain growth. Modell Sim Mater Sci Eng. 2014;22:025028. doi: 10.1088/0965-0393/22/2/025028
79.
ZöllnerD.A phenomenological approach to investigate nanocrystalline grain growth. Comput Mater Sci. 2014;92:114–119. doi: 10.1016/j.commatsci.2014.05.026
80.
ZöllnerD.Grain microstructural evolution in 2D and 3D polycrystals under triple junction energy and mobility control. Comput Mater Sci. 2016;118:325–337. doi: 10.1016/j.commatsci.2016.03.031
81.
ZöllnerD, RiosPR.Investigating the von Neumann-Mullins relation under triple junction dragging. Acta Mater. 2014;70:290–297. doi: 10.1016/j.actamat.2014.02.039
82.
RiosPR, GlicksmanME.Grain boundary, triple junction and quadruple point mobility controlled normal grain growth. Phil Mag. 2015;95:2092–2127. doi: 10.1080/14786435.2015.1050476
83.
NovikovVY.On the influence of triple junctions on grain growth kinetics and microstructure evolution in 2D polycrystals. Scripta Mater. 2005;52:857–861. doi: 10.1016/j.scriptamat.2005.01.013
84.
GottsteinG, ShvindlermanLS.Grain boundary junction engineering. Scripta Mater. 2006;54:1065–1070. doi: 10.1016/j.scriptamat.2005.11.057
85.
KrillCEIII, HelfenL, MichelsD, Size-dependent grain-growth kinetics observed in nanocrystalline Fe. Phys Rev Lett. 2001;86:842–845. doi: 10.1103/PhysRevLett.86.842
86.
RaneGK, WelzelU, MittemeijerEJ.Grain growth studies on nanocrystalline Ni powder. Acta Mater. 2012;60:7011–7023. doi: 10.1016/j.actamat.2012.08.059
87.
AmesM, MarkmannJ, KarosR, Unraveling the nature of room temperature grain growth in nanocrystalline materials. Acta Mater. 2008;56:4255–4266. doi: 10.1016/j.actamat.2008.04.051
88.
PaulH.The thermal instability of nanocrystalline materials - an experimental case study of microstructural evolution in ball-milled iron [Ph.D. Thesis].
Germany: Ulm University, 2012.
89.
MullinsWW.The effect of thermal grooving on grain boundary motion. Acta Metall. 1958;6:414–427. doi: 10.1016/0001-6160(58)90020-8
90.
BarmakK, EggelingE, SharpR, Grain growth and the puzzle of its stagnation in thin films: a detailed comparison of experiments and simulations. Mater Sci. Forum. 2012;715-716:473–479.
91.
BarmakK, EggelingE, KinderlehrerD, Grain growth and the puzzle of its stagnation in thin films: the curious tale of a tail and an ear. Progr Mater Sci. 2013;58:987–1055. doi: 10.1016/j.pmatsci.2013.03.004
92.
ZöllnerD.Treating grain growth in thin films in three dimensions: a simulation study. Comput Mater Sci. 2016;125:51–60. doi: 10.1016/j.commatsci.2016.08.026
