Twin boundaries with 9R zone in Cu and Ag studied by quantitative HRTEM

Abstract

When highly inclined against the {111} plane of the coherent twin boundary, ∑3 〈110〉 tilt boundaries in Cu or Ag have a complex structure. As the boundary plane approaches the symmetrical {211} orientation, the grain boundaries decompose into two phase boundaries. Between these phase boundaries the metal adopts a rhombohedral crystal structure, denoted as 9R. Not the {211}-oriented boundary, but a boundary inclined by ≈8° against {211} has the minimum energy in this family of grain boundaries with 9R zone. Using high resolution transmission electron microscopy, we have studied the atomistic structure of this special boundary. An iterative structure refinement based on quantitative image analysis reveals the atomistic structure of the grain boundary at a well-defined level of confidence. Comparing the refined grain boundary structure with a model obtained by molecular statics calculations exposes small, but significant discrepancies. These probably arise because in the model the stacking fault energy is too small and the short distance repulsion is too weak. Grain boundaries of equivalent geometry in Ag and Al exhibit different widths of the 9R zone. Experimental observations support a theory relating the equilibrium width of the 9R slab to the stacking fault energy and the elastic properties of the material.