Bicrystal

The geometry of interfaces

The simplest interface is a single isolated planar interface separating two otherwise perfect crystals of the same, or different, crystalline phases, that is, a planar interface in a bicrystal. Just as the concept of a perfect single crystal is the basis for all discussion of point and line defects and elementary excitations in crystalline matter, so the concept of an ideal bicrystal containing a planar interface is an essential experimental and theoretical tool for understanding the properties of interfaces.

The translational and orientational order that exists in the adjoining crystals of a bicrystal is the source of all structural order that may exist in the interface. Bicrystallography is concerned with the symmetries characterizing the structural order that exists in a bicrystal.


The relationship between two crystals

A lattice is a set of vectors that is closed under addition and subtraction: the sum and difference of any two vectors in the set are also in the set. When there exists a shortest length vector in the lattice the lattice is described as periodic; otherwise, it is described as quasiperiodic. A crystal is obtained by decorating each lattice site of a periodic lattice with a basis comprising one or more atoms arranged in an identical fashion. The symmetry of the crystal can, therefore, be lower than that of its lattice, eg. Each lattice site is an inversion centre in the lattice but not necessarily in the crystal. If the crystals on either side of an interface have the same chemical composition and structure the interface is of the homophase type. Heterophase interfaces separate crystals of differing composition and/or structure. heterophase interfaces appear, for example, in first order phase transformations where a new phase nucleates and grows within an existing phase. Common examples of homophase interfaces are grain boundaries separating identical crystals with differing orientations, inversion boundaries, and stacking faults.
If a crystal space group does not contain mirror glide planes or screw rotation axes it is described as symmorphic. Non-symmorphic operations are characterized by the requirement of a supplementary displacement, that is not a lattice vector, in addition to a point group operation such as a rotation or reflection. If a crystal contains a centre of inversion it is described as centrosymmetric. Some crystals display rotational symmetries that are combined with inversion operations; such operations are called improper rotations. Crystals that do not contain any mirror planes or an inversion centre may have a handedness and exist in enantiomorphic pairs. When we describe the relationship between two crystals we may use any linear transformation that is not a symmetry operation of either crystal, including inversions, mirror reflections, improper rotations, proper rotations, and homogeneous deformations. Exceptionally, the supplementary displacement, associated with a non-symmorphic operation relating two crystals, may be ignored because it could be argued that he crystals meeting at the interface will translate with respect to each other so as to minimize the interfacial energy. The supplementary displacement then becomes incorporated into this relative translation.

Sutton A P, Balluffi R W, (1996), Interfaces in Crystalline Materials, Clarendon Press Oxford




While there are many techniques in TEM that can be used to analyse interfaces and defects, it is perhaps the combination of atomic resolution Z-contrast imaging and electron energy loss spectroscopy EELS in the scanning transmission electron microscope STEM that offers t he greatest potential to unravel the complexities of the structure property relationships. STEM Application, oxfordjournals.org