five-folded and seven-folded disclinations. This two step melting is described within the so-called Kosterlitz-Thouless-Halperin-Nelson-Young-theory (KTHNY theory), based on two transitions of Kosterlitz-Thouless-type. Observation Transmission electron microscopy (TEM) Transmission electron microscopy can be used to observe dislocations within the microstructure of the material. Thin foils of material are prepared to render them transparent to the electron beam of the microscope. The electron beam undergoes diffraction by the regular crystal lattice planes into a diffraction pattern and contrast is generated in the image by this diffraction (as well as by thickness variations, varying strain, and other mechanisms). Dislocations have different local atomic structure and produce a strain field, and therefore will cause the electrons in the microscope to scatter in different ways. Note the characteristic 'wiggly' contrast of the dislocation lines as they pass through the thickness of the material in the figure (also note that dislocations cannot end in a crystal, and these dislocations are terminating at the surfaces since the image is a 2D projection). Dislocations do not have random structures, the local atomic structure of a dislocation is determined by the Burgers vector. One very useful application of the TEM in dislocation imaging is the ability to experimentally determine the Burgers vector. Determination of the Burgers vector is achieved by what is known as ("g dot b") analysis. When performing dark field microscopy with the TEM, a diffracted spot is selected to form the image (as mentioned before, lattice planes diffract the beam into spots), and the image is formed using only electrons that were diffracted by the plane responsible for that diffraction spot. The vector in the diffraction pattern from the transmitted spot to the diffracted spot is the vector. The contrast of a dislocation is scaled by a factor of the dot product of this vector and the Burgers vector (). As a result, if the Burgers vector and vector are perpendicular, there will be no signal from the dislocation and the dislocation will not appear at all in the image. Therefore, by examining different dark field images formed from spots with different g vectors, the Burgers vector can be determined. Other methods Field ion microscopy and atom probe techniques offer methods of producing much higher magnifications (typically 3 million times and above) and permit the observation of dislocations at an atomic level. Where surface relief can be resolved to the level of an atomic step, screw