Twinning boundary energy

Similar relations can be used to find the twin boundary energy from the grain boundary energy and the boundary energy between two phases from the energy of a grain boundary in one of them. 

However, it is not yet clear why the ener es of the SISF and the twin boundary increase with increasing A1 concentration. To find a clue to the problem, it would be needed to make out the effects of the short-range ordering of A1 atoms in excess of the stoichiometric composition of the HAl phase on the energies of planar faults and the stmcture of dislocation cores in the Al-rich HAl phase. 

All real crystals have atoms which occupy external surface sites and which do not possess the correct number of nearest neighbors as a consequence, Thus, a surface is a scat of energy and is characterized by surface tension. Furthermore, internal surfaces exist, grain boundaries and twin boundaries across which atoms are incorrectly positioned. In a crystal of reasonable size—say 1 cubic centimeter, these two-dimensional defects, called surface defects, contain only about 1 atom in 106, a rather small fraction. Even so, surfaces are important attributes of solids. 

The surface energy of a twin boundary in copper is about 20 mJ/m.2... 

Like a grain boundary, the twin boundary is a higher energy state, relative to the crystal. However, because a twin boundary is highly ordered, it is of lower energy than... 

A second type of boundary, in which there is no misorientation between grains, is the antiphase boundary. This occurs when wrong atoms are next to each other on the boundary plane. For example, with hexagonal close-packed (HCP) crystals, the sequence. .. ABABAB... can be reversed at the boundary to ABABA ABABA, where represents the boundary plane. Antiphase boundaries and stacking faults are typically of very low energy, comparable to that of a coherent twin boundary. 

In addition, decahedral nanoparticles are strained. This is because the preferred angle between the twin planes is 70.5°, yet 72° is available [58]. Thus, a total of 7.5° needs to be filled by strain of the crystal lattice. As a result, the twin boundaries represent high energy sites that may promote growth at the uncoated 111 end faces. 

The observation that single pericline boundaries are commonly replaced by a large number of albite twin boundaries, possibly involving a l(X)-fold increase in total area of twin boundary per unit volume, suggests that the energy of a pericline twin boundary is greater than that of an albite twin boundary by a similar factor at normal temperatures (see later). 

The second key observation is that the intersections between a twin boundary and a crystal surface represent chemically activated sites (and mechanically soft areas) (Novak and Salje 1998a, 1998b). It appears safe to assume that similarly activated sites exist also at the intersection of APBs and dislocations with the surface (e.g. Lee et al. 1998, Hochella and Banfield 1995). Besides the obvious consequences for the leaching behaviour of minerals, these key observations lead to the hypothesis of confined chemical reactions inside mesoscopic patterns. The idea is as follows as the surface energy is changed near mesoscopic interfaces, dopant atoms and molecules can be anchored near such interfaces. Some particles will diffuse into the mineral and react with... 

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