Crystallography of Grain Boundary Networks

An extensive range of material properties depend strongly on the character and topology of grain boundaries, including both intergranular and transgranular phenomena.  For example, intergranular corrosion follows a connected channel of susceptible grain boundaries, while cleavage cracks follow specific crystallographic planes and change direction when they encounter grain boundaries.  One unified approach to link the details of microstructural topology with these properties is to study the connectivity of different boundary types in the grain boundary network.  From the perspective of the network as a whole, this is formulated as a percolation problem.  Standard percolation theory is based on the assumption that bonds (grain boundaries in the present case) may be randomly assigned as resistant or susceptible.  However, the assumption of a randomly-assembled lattice turns out to be critically flawed in the case of grain boundary networks, due to local correlations imposed by crystallographic consistency.  The distribution of grain boundaries in (a) and (b) of the figure below are random, with no preferred grouping of boundaries beyond that expected in a random network. In contrast, the high angle boundaries in (c) of the figure tend to form stringy structures with a longer connectivity length than in the random lattice, and the low angle boundaries in (d) of the figure form small clusters that prefer to have many “dangling bonds.”  The global behavior of the boundary network is therefore governed by local crystallographic effects, particularly at grain boundary junctions. Analytical expressions for the triple-junction types present in the grain boundary network have only recently been found by our group for two-dimensional fiber textured materials; one direction of our current research is extending this solution to more general textures in three-dimensional materials.

See also the recent Viewpoint Set on Grain Boundary Engineering in Scripta Materialia

Grain boundary networks in which the grain boundaries are either randomly assigned (a and b), or assigned in a crystallographically consistent manner (c and d). The high angle boundaries are shown in red (a and c), while the low angle boundaries from the same network are shown in green (b and d).

Published Articles:

Correlated grain-boundary distributions in two-dimensional networks
Mason JK, Schuh CA; ACTA CRYSTALLOGRAPHICA SECTION A 63: 315-328 Part 4 JUL 2007 (PDF)

Correlations beyond the nearest-neighbor level in grain boundary networks
Schuh CA, Frary M; SCRIPTA MATERIALIA 54 (6): 1023-1028 MAR 2006 (PDF)

Grain boundary networks: Scaling laws, preferred cluster structure, and their implications for grain boundary engineering
Frary M, Schuh CA; ACTA MATERIALIA 53 (16): 4323-4335 SEP 2005 (PDF)

Connectivity and percolation behaviour of grain boundary networks in three dimensions
Frary M, Schuh CA; PHILOSOPHICAL MAGAZINE 85 (11): 1123-1143 APR 2005 (PDF)

Universal features of grain boundary networks in FCC materials
Schuh CA, Kumar M, King WE; JOURNAL OF MATERIALS SCIENCE 40 (4): 847-852 FEB 2005 (PDF)

Percolation and statistical properties of low- and high-angle interface networks in polycrystalline ensembles
Frary M, Schuh CA; PHYSICAL REVIEW B 69 (13): Art. No. 134115 APR 2004 (PDF)

Nonrandom percolation behavior of grain boundary networks in high-T_c superconductors
Frary M, Schuh CA; APPLIED PHYSICS LETTERS 83 (18): 3755-3757 NOV 2003 (PDF)

Combination rule for deviant CSL grain boundaries at triple junctions
Frary A, Schuh CA; ACTA MATERIALIA 51 (13): 3731-3743 AUG 2003 (PDF)