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A determination of the surface tension and surface migration constants of metals in the solid phase, based on the use of pulsed Geld emission microscopy, is discussed. The experimental technique is described. An application to 6eld emission cathodes of Herring's theory of transport phenomena in solids is given, which yields the necessary relations required for the determination of the basic physical constants from the experimental data. Results are presented and discussed for the case of tungsten. The method is applicable to a number of other metals, several of which are currently under investigation. I. INTRODUCTIOÑ'RANSPORT phenomena are known to occur in heated solids. Several physical processes may be involved, such as volume diGusion, evaporation and condensation, or plastic Row; the dominant process is determined by the experimental conditions, particularly the temperature and the size of the object under study. The experimental determination of the physical constants associated with transport phenomena provides , basic information concerning the solid state; studies concerning refractory metals have a practical signiGcance related to their use as cathode materials.The evaporation of tungsten was studied some time ago by Zwikker. ' More recently, tracer techniques have been used to investigate the volume self-diffusion of various metals, e.g. , tantalum. ' The surface migration of numerous combinations of impurities on base metals has been investigated with Geld emission microscopy. 'Recently, an intermediate temperature has been used to maintain the electrical stability and longevity of pulsed field emitters4; under such conditions, the tungsten emitter may change its shape by a transport mechanism which has been identiGed as surface migration. 'The choice of operating conditions requires a knowledge of the diffusion constants and surface tension. Each of these constants may be determined with good accuracy through the measurement of the rate of change of cathode geometry. In an early experiment Muller' obtained an indirect determination of the geometric change from the corresponding change in the field emission current-voltage relationship, and deduced values for the activation energy and the diff'usivity constant; uncertainties were introduced in these measurements by the lack of a sensitive method for the direct measurement of small geometrical changes, and by the inability to determine the emitter geometry accurately by direct observation.Pulsed T-F emission microscopy' provides a considerably more sensitive method by which the rate of surface migration can be directly measured during the transport of a sufficiently small volume of material that the gross cathode geometry remains essentially unchanged. Other advantages of the method include a controlled and favorable cathode geometry, excellent depth resolution and high magni6cation, and continuous monitoring through the emission pattern of the surface under study. The present paper reports the use of this method to obtain improved values of the activa...

When a specially designed field cathode assembly was inserted in a commercial electron microscope which was appropriately modified for the purpose, the geometry of the needle shaped emitter was obtained from micrographs of several of its profiles at various stages of emitter fabrication and experimental use. An investigation of several methods of fabrication revealed that a smooth, simple, and relatively stable tungsten emitter geometry resulted from a refinement of the methods of Benjamin and Jenkins which combines the electrolytic etch and the smoothing action of surface migration. The electric field at any point on an emitter surface was calculated when the emitter geometry was precisely fitted with one equipotential surface from the family surrounding a charged, isolated sphere-on-orthogonal-cone. A theoretical surface distribution of current density for a typical emitter was derived from the calculated field distribution and the wave-mechanical field emission theory. From this result was calculated a value of the emitting area which was in good agreement with experiment.

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