Triple lines in materials science and engineering

doi:10.1016/j.scriptamat.2010.02.020

Scripta Materialia

Volume 62, Issue 12, June 2010, Pages 889-893

https://doi.org/10.1016/j.scriptamat.2010.02.020 Get rights and content

Abstract

We assess the impact of triple lines in materials preparation and use by considering several examples of materials behavior in which they have identifiable effects. The microstructural roles of triple lines are also considered and some persistent scientific questions are raised.

Introduction

Research on surfaces and interfaces in materials emerged throughout the twentieth century as an extension of the study of uniform solid and liquid phases. The study of triple lines is a natural extension of the study of surfaces and interfaces.

Condensed phases have often been studied using theoretical formulations that assume specimens that have infinite extent. Crystallographic analysis is only one simple case in point: a crystal lattice, by definition, is infinite in all directions. Real crystals, however, have surfaces and interfaces, and the properties of these crystallographic “defects” can have profound influences on the properties and behavior of the materials. The electronic and optical properties, chemical homogeneity, mechanical behavior, kinetics and even the shape of a piece of material are all affected by its surfaces and internal interfaces. Research on surfaces and interfaces has been driven by the need to understand their behavior, in order to understand real materials.

In many cases, particularly for internal grain boundaries, early theoretical treatments were also based upon structures that extend infinitely in two dimensions. The classic Read–Shockley model for grain boundary energy, for example, produces simple results only if the periodic grain boundary structure is infinite [1]. Computer simulation algorithms are almost always constructed to mimic infinitely extended interfaces by means of computational cells with periodic boundary conditions. Finite boundaries are rather more complicated to deal with [2], but just as a crystal must be bounded by surfaces or grain boundaries, a surface or an interface must either close upon itself or be bounded by triple lines. If those triple lines have anything more than trivial properties, then they can affect the behavior of the interfaces that they bound.

One view of the “materials science” approach to understanding the properties of condensed matter is that it starts with infinite continuum theoretical treatments, then adds the effects of surfaces, interfaces and other imperfections. In this paper, and this colloquium, we will explore cases in which triple lines exert influence upon the interfaces to which they are connected, and thus affect the properties of their host materials.

Section snippets

Practical effects and uses of triple lines

Triple junctions have direct impacts on the uses and applications of certain engineering materials. Some of these are described here, to set the stage for a description of their effects on materials processing, eventually leading to the basic science of triple lines.

The most familiar effects associated with triple lines relate to wetting and dewetting, where the contact angles between three phases are related to the effective interfacial energies, according to the Herring equation: $\sum_{i = 1}^{3} γ_{i} τ_{i} + \sum i = 1$

Impacts of triple lines on materials behavior

Triple lines have a number of impacts on materials behaviors that are of greater interest to materials scientists than to the engineers who need to use the materials. In the following aspects of triple line behavior, their impacts on the internal processes of polycrystalline materials are the particular focus.

One of the earliest studies of triple junctions in materials was the analysis of the groove formed at the intersection of a grain boundary with a surface [12]. The shape of the surface

Understanding triple lines

Materials with nanoscaled microstructures tend to magnify the importance of triple lines, which represent an increasing fraction of the volume of the material as size decreases, as indicated in Figure 5 [28], [29]. It is probably misleading, however, to assign importance based upon the volume fraction: grain boundaries represent a very small volume fraction at conventional grain sizes, but their influence is still unmistakable. Similarly, Gottstein and Shvindlerman [30] have shown that, even

Summarizing remarks

Despite their evident impact upon the science and engineering of materials – especially of polycrystalline materials – the specific behaviors of triple lines remain relatively poorly studied. Several basic properties remain unknown, and research directed specifically at understanding triple lines is still very much in its infancy.

Acknowledgement

The author acknowledges the support of the Ames Laboratory, which is operated by Iowa State University of Science and Technology for the U.S. Department of Energy under contract No. DE-AC02-07CH11358.

References (39)

K. Landry et al.
Acta Mater.
(1997)
H. Kim et al.
Acta Mater.
(2009)
F.Y. Genin
Acta Metall. Mater.
(1995)
W.W. Mullins
Acta Metall.
(1958)
G. Gottstein et al.
Acta Mater.
(2000)
B. Bokstein et al.
Mater. Sci. Eng. A
(2001)
T.P. Swiler et al.
Mater. Sci. Eng. A
(1997)
K. Owusu-Boahen et al.
Acta Mater.
(2001)
F. Lefevre-Schlick et al.
Mater. Sci. Eng. A
(2009)
G. Palumbo et al.
Scr. Metall. Materialia
(1990)

G. Gottstein et al.

Acta Mater.

(2002)

S. Shekhar et al.

Acta Mater.

(2008)

S.G. Srinivasan et al.

Acta Mater.

(1999)

W.T. Read et al.

Phys. Rev.

(1950)

A.H. King et al.

Mater. Sci. Forum

(1995)

C. Herring

J.A. Howarter et al.

Macromol. Rapid Commun.

(2008)

J. Xu et al.

Phys. Rev. Lett.

(2006)

C.W. Extrand

Langmuir

(2002)

Cited by (37)

Wandering and nanolaminated structures of grain boundary triple junctions in tungsten
2020, Materials Letters
The peculiarities of nanomorphology triple junctions have been studied by the method of field ion microscopy in fine-grained high-textured tungsten using the phenomenon of atom-by-atom field evaporation. It was found evidence of the formation of double-kinks at the triple junction lines accompanied by a local intrusion of several atomic layers of one grain into another. Observed a double-kink mode of the wandering is geometrically related to revealed nanolaminated structures of triple junctions bounded by pairs of twist boundaries. Molecular statics calculations have shown that the grain boundary expansion and energetics for the laminated grains with incommensurate twist grain boundaries are essentially independent of their thickness in nano-scale region.
Effects of coherency strain on structure and migration of a coherent grain boundary in Cu
2019, Materials Characterization
Citation Excerpt :
It is tacitly accepted that these driving forces apply whether a GB is incoherent or coherent. In a polycrystal, GBs are connected to each other through triple lines and quadruple points and thus the migration of a GB will influence that of others [4–7]. A polycrystal is thus regarded as a network of GBs, either incoherent or coherent.
In situ high-resolution transmission electron microscopy of atomic structures of a coherent grain boundary is reported in a Cu bicrystal specimen composed of two grains with surface normal directions of [1 0 0] and [1 1 0]. Although the surface energy anisotropy favors the growth of the [1 0 0]-oriented grain, grain-boundary migration does not occur. Instead, inside the [1 0 0]-oriented grain standing off the grain boundary is a kind of coherent interface observed. We relate these observations to the development of a coherent strain due to a lattice misfit at the grain boundary.
Study the grain boundary triple junction segregation of phosphorus in a nickel-base alloy using energy dispersive X-ray spectroscopy on a transmission electron microscope
2019, Materials Characterization
Citation Excerpt :
Compared with GB segregation, segregation of P to GB triple junctions (TJs) has rarely been reported [8]. TJs, as line defects in their own right with specific kinetic and thermodynamic properties, have received some attentions recently [9,10]. They can act as fast diffusion path due to the larger free volume compared with grain boundary, which has been confirmed by diffusion experiments and molecular dynamics modeling [10–14].
Segregation of phosphorus at grain boundary triple junctions in a nickel-base alloy was measured using energy dispersive X-ray spectroscopy on a transmission electron microscope. It was found that the triple junction segregation of phosphorus varies with grain boundaries in that the concentration of phosphorus at triple junction can be higher or lower than that at the adjacent grain boundaries. A concentration gradient was detected along some grain boundaries within a distance of 5–100 nm from the associated triple junctions. The results are discussed with regards to various structural and atomistic diffusion characteristics.
Evidence for Bingham plastic boundary layers in shear banding of metals
2018, Extreme Mechanics Letters
We study material flow in the vicinity of single shear bands in high strain-rate ( $1 0^{4}$ – $1 0^{5}$ per second) deformation of metals. Shear band plastic flow, in three different materials, is shown to resemble unsteady planar Couette flow (Stokes first problem) of a Bingham fluid. Equivalent shear band viscosities and yield stresses are obtained, with the former similar to liquid metal viscosities and the latter being $\sim 0.5$ times the band nucleation stress. Reynolds and Bingham numbers, computed based on the shear band displacement measurements, are suggestive of boundary layer formation, consistent with the severe localization of deformation within shear bands.
Embedded-atom study of grain boundary segregation and grain boundary free energy in nanosized iron–chromium tricrystals
2018, Acta Materialia
Citation Excerpt :
Since the GBs terminate with a disproportionately high density of segregation sites at the TJ (red structural units in Fig. 4(b)), these additional sites of iron now translate into a negative value for the TJ excess, as can be seen for the lower temperatures from 600 K to 800 K on the chromium-rich side in Fig. 11. We want to mention that this effect is a unique feature of this particular TJ [34]. Certainly, it does depend on the actual structure of the considered TJ and joining GBs.
We present a theoretical study of equilibrium grain boundary (GB) segregation in a tricrystal setup using a thermodynamically accurate iron–chromium embedded-atom potential. Through continuous variation of the chemical potentials, the full concentration range is explored in the temperature range of 600 K–1100 K, evaluating segregation below and above the critical temperature of the miscibility gap. Key findings are: i) the GB excess entropy is rather small and shows only weak variation with temperature; ii) due to the small lattice mismatch in the iron–chromium system, segregation can reasonably be predicted by comparing the $T = 0$ energies of iron and chromium; iii) every atomic site in the defects undergoes the occupation probability transition at a different chemical potential, resulting in stepwise segregation isotherms; iv) the extraordinary thermodynamic properties of the iron–chromium system lead to negative GB free energies on the chromium-rich side; v) the width of the GB segregation zone decreases with temperature and depends significantly on the bulk concentration; vi) the additional triple junction (TJ) excess segregation is small relative to the GBs and for the most part a geometric effect of the finite width of the GB segregation zones. Available experimental data of GB segregation on the iron-rich side are in good quantitative agreement with the presented results.
Effect of Al content on magnetic properties of Fe-Al Non-oriented electrical steel
2017, Journal of Magnetism and Magnetic Materials
The effects of Al content (0.53 ≤ Al ≤ 9.65 wt%) on microstructure, texture, magnetic flux density, permeability, core loss and magnetic domain structure of Fe-Al based electrical steel were measured or observed. Average grain size decreased as Al content increased, but Al contents had no severe effects on texture. Magnetic flux density and permeability tends to decrease as Al content increased. Total core loss P_tot was separated into hysteresis loss P_h, eddy-current loss P_e and anomalous loss P_a. As Al increased, P_h increased, but P_e and P_a decreased, so the optimal grain size increased. To reduce core loss of electrical steel with high resistivity, annealing should be conducted at high temperature and for a long time to increase grain size.

View all citing articles on Scopus

View full text

Viewpoint PaperTriple lines in materials science and engineering

Abstract

Introduction

Section snippets

Practical effects and uses of triple lines

Impacts of triple lines on materials behavior

Understanding triple lines

Summarizing remarks

Acknowledgement

Acta Mater.

Acta Mater.

Acta Metall. Mater.

Acta Metall.

Acta Mater.

Mater. Sci. Eng. A

Mater. Sci. Eng. A

Acta Mater.

Mater. Sci. Eng. A

Scr. Metall. Materialia

Acta Mater.

Acta Mater.

Acta Mater.

Phys. Rev.

Mater. Sci. Forum

Macromol. Rapid Commun.

Phys. Rev. Lett.

Langmuir

Viewpoint Paper
Triple lines in materials science and engineering