A. Müller’s research while affiliated with Fritz Haber Institute of the Max Planck Society and other places

To determine the temperature of a heated crystal in a field electron or ion microscope, not only the temperature of the heated loop, but also the temperature gradient along the emitter tip due to heat conduction and radiation must be considered. A method is described to calculate the temperature distribution along the tip. Typical numerical results are given for tips of tungsten and some other metals at temperatures between 1000 and 2900 °K. Considered are conical tips of different length (half cone angle between 0.5° and 6°) and some non-conical tips. The temperature gradient near the apex (which influences the shape change by surface diffusion) has a maximum for a particular angle of the conical tip. Very high gradients occur at tip constrictions.

The field ion microscope was used for measuring the surface free energy anisotropy of tungsten. Tips with a long shank and a small cone angle (< 1.6°) were annealed in ultra high vacuum at 2600°K in order to obtain small crystals with a clean surface. The radius of these tips remained below 2000Å. The equilibrium shape is assumed to be present if — for a certain time, in spite of strong surface diffusion — annealing of the crystal does not lead to any further measurable shape change. The form of a crystal thus treated was determined from its field ion image with corrections due to local variation of magnification. The magnification depends among other things on the local radius of curvature, which was determined by the measured “best-image” voltage of each surface region. From the crystal shape thus obtained, the surface energy anisotropy of the zones [111], [100], and [110] was determined according to the construction of Wulff. The anisotropy values are more precise than those determined from field electron micrographs. The experimental anisotropy values are compared with 3 types of calculated data. A certain qualitative agreement exists with the data of Stranski and Suhrmann. The agreement is better with the Morse potential data of Drechsler and Nicholas. Quantitative agreement, however, is found only with the Mie potential anisotropy of Drechsler and Nicholas.If the surface of tungsten is covered with an adsorption layer during annealing, a different crystal shape is formed by means of surface diffusion.