R. Uzan

Tip shape evolution: Capillarity-induced matter transport by surface diffusion. I

Abstract From basic equations describing physical phenomena occuring at different temperatures, we have calculated numerically the matter transport by surface diffusion alone or by simultaneous action of surface diffusion and evaporation. Tip morphological evolution is then obtained by computer simulation for different cone angles and for different temperatures. Theoretical results show a critical cone angle. For tips with cone angles below this critical value a solid drop formation and detachment is observed at the tip end. For angles greater than this critical value two cases must be considered. First, for matter transport by surface diffusion only, steady-state profile evolution is predicted; such an evolution follows the Herring scaling law t 1 4 . Second, in the case of simultaneous action of surface diffusion and evaporation and for these high angles, calculations show tip evolution toward pseudo-stationary profiles; these profiles are characteristic of each cone angle, but their geometrical dimensions are function of the heating conditions (i.e. surface diffusion and evaporation values). Equations for the variations of the tip apex radius as function of surface diffusion coefficient and evaporation rate are deduced for these two cases, as well as variations of geometrical constants as a function of tip half-cone angles.

Grain boundary groove evolutions by surface self-diffusion on a plane and on a wire

Abstract Experiments on the evolution of the profile of metallic filaments of small diameter and tips show certain discrepancies with the known theoretical descriptions of grainboundaries grooving. According to our hypothesis, these discrepancies are due to the fact that the former calculations were made only for the case of a plane and not for a cylindric surface. Therefore, using a modified method we have calculated the grooving evolution for a plane as well as for a wire. The main results for a plane are more or less in accordance with former calculations. The main results for a wire are: (a) the groove profile evolution is not any more steady-state; (b) the groove depth increases more rapidly han in the case of a plane; (c) the mean groove angle is not any more constant, but varies with time (while the difficult observable equilibrium angle stays constant); (d) the profile evolution leads to a new phenomenon: the wire will be divided into two parts only by surface migration. Electron microscope observations of groove shapes on wires and tip shanks, are qualitatively in agreement with the presented calculated results.

Une détermination du coefficient d'auto-diffusion de surface avec des pointes à émission de champ (tungstène)

Abstract To measure the surface self-diffusion coefficient, a method is described which is based on the increase of the curvature radius of a tip (Nichols and Mullins). This radius increase depending on temperature and time is measured under ultra high vacuum condition. The cleanliness of the surface is controlled by field electron microscopy. The radius variation is measured in situ by Fowler-Nordheim characteristics, and the initial and final radius by scanning electron microscopy. Measured are, for tungsten between 2100 and 2850°K, the activation energy ( 3.1 eV atome ) and the diffusivity ( 0.9 cm 2 s ) .

Grain boundary grooving under the influence of evaporation (or corrosion)

Known grain boundary grooving theories have considered three mechanisms—surface diffusion, volume diffusion and evaporation-condensation—acting either alone (Mullins, Robertson) or in concomitance (Mullins, Srinivasan and Trivedi). We present here a grooving theory in which a loss of matter (free evaporation or corrosion) is considered simultaneously with surface diffusion. A dimensionless parameter S is introduced which represents the relative weight of surface diffusion and free evaporation. Surface profile evolutions are calculated as a function of S. As the consequences of the effect of free evaporation: (1) The groove evolution is not any more a steady-state profile evolution. The grooving speed is reduced and the ratio between the ridge height and the groove depth is increased. (2) The groove profile leads to an apparent limiting groove profile whose geometry is a function of S. (3) The time needed for the formation of this apparent limiting groove profile is a function of the diffusion coefficient, the free evaporation rate and the equilibrium groove angle. (4) Thereafter the groove evolution is pseudostationary. Calculations are made for initial plane surface and initial cylindric surface. The former theories (Mullins, Robertson) must be replaced by the described theory in particular if the free evaporation rate (or corrosion), which depends on temperature and substance, is not negligible. The results of the theory are compared with known experimental data, mainly those of Allen. Characteristics of the experimental results can be easily explained by the described theory which should then replace former interpretations for the observed deviations from the steady-state evolution theories. The presented theory opens the possibility to measure the surface diffusion coefficient in regions where evaporation or corrosion occurs and enables one to measure the distribution of parameters of evaporation and corrosion along a great surface area.

Adsorption, diffusion and self-diffusion on tungsten surfaces with adsorbed palladium

The influence of a Pd adsorption layer on the surface self-diffusion of tungsten has been measured using a field emitter technique. By adsorption of 1.2 × 1015 Pd atoms/cm2 — measured by high energy ion backscattering — the surface self-diffusion energy decreases from 70 to 54 kcal/mole, and the diffusivity from 0.95 to about 0.2 cm2/s, which corresponds to an increase of the diffusion coefficient by a factor 40 at 1600 K and 80 at 1400 K. Furthermore are determined (1) adsorption lifetimes in adsorption-desorption equilibria, (2) the isosteric adsorption heat (103 kcal/mole), and (3) the coefficient of Pd surface diffusion on W resulting in diffusion energies of 32 kcal/mole around (001) and 17 kcal/mole around (111).

Une détermination du coefficient d'autodiffusion de surface en présence d'une couche d'adsorption à l'aide de pointes àémission de champ (nickel sur tungsténe)

The tip blunting technique to measure the surface self-diffusion of clean metals (A. Piquet, Vu Thien Binh, H. Roux, R. Uzan and M. Drechsler) is extended to study the influence of an adsorption layer on diffusion. The system studied is nickel on tungsten. The increase of the apex radius is measured by means of FEM characteristics. In the temperature range used (1200–1500 K), the nickel monolayer (1.16 × 1015 atoms/cm2) is maintained by compensation of desorbed Ni atoms with a continual flux from an evaporation source. The adsorption life time between 1350 and 1500 K decreases from 850 to 16 s. The conservation of the degree of coverage leads to a method to determine the desorption activation energy of nickel (Ed = 4.56 eV/atom). The surface self-diffusion data of tungsten with a nickel monolayer are found to be D0 = 3 × 10−3cm/2s and Qs = 1.9 eV/atom, compared to the clean tungsten data D0 = 1 cm2/s and Qs = 3.1 eV/atom. The Ni monolayer increases the surface self-diffusion coefficient by a factor 160 at 1200 K and 20 at 1500 K. The results are discussed with respect to nickel activated sintering of tungsten powders.

Processus simultane d'évaporation libre et de diffusion de surface☆

Abstract If a conical metal tip is annealed in vacuum, the radius at the apex increases with time by surface diffusion. This was calculated by Nichols and Mullins and recently verified by the authors. This phenomenon is now calculated in case of a simultaneous action of evaporation and surface diffusion. By evaporation the blunting rate should be lowered until it becomes zero for a critical value of the curvature radius. Numerical data for different temperatures and cone angles are calculated for some metals (W, Mo, Pt, Ni, Cu). Measured are profile changes of Mo tips during annealing. The lowering of the blunting rate and the existence of a limit radius are confirmed. An evaporation can also occur as a consequence of a surface reaction. The measured radius changes of tungsten tips annealled in 1.5 × 10 −5 torr and 2.5 × 10 −5 torr of oxygen agree fairly well with the predictions. Surface self-diffusion measurements at high temperatures may be erroneous if evaporation is not considered, an example for Mo at 2150°K is given.

A measurement of surface diffusion across steps on a curved surface (Pd on W)

Abstract The surface diffusion of palladium on the curved part of a tungsten crystal is studied by field electron microscopy. The variation of the local coverage distribution is measured by a probe-hole device on the stepped surface region around (001). The measured data allow a determination of the mass transport surface diffusion coefficient D of Pd on W across atomic steps as a function of temperature, coverage and step density. D has been found (1) to be constant for a given step density and for coverages lower than about 5 × 10 14 Pd adatoms/cm 2 , (2) to increase for higher coverages, and (3) to increase with increasing step density for a given coverage. The activation energy of the process is nearly constant (about 24 kcal/mol) for all coverages up to about 6 × 10 14 adatoms/cm 2 , while the pre-exponential factor of D increases with increasing step density. Interpretation of the results gives some information on the diffusion mechanism.

Electronic structure of selenium aggregates by a self-consistent method including 4d orbitals

The electronic structure of small selenium aggregates Sen > (2 < n < 10) has been calculated using the CNDO method on a complete basis 4s, 4p, 4d. The energy per bond, the ionization potentials (IP) and the electronic affinities (EA) are given as a function of the aggregate size. The IP and EA converge to a common value which approaches the work function of bulk metal. The calculated gap is in good agreement with recent experimental determinations.

A determination of the rate and heat of evaporation by measuring the radius variations of a metal tip

Abstract A new material loss technique for the experimental determination of the free evaporation rate of a metal is presented. This technique is based on the study of tip profile changes. The tip radius variation is a consequence of the simultaneous action of free evaporation and surface self-diffusion. The rate of free evaporation is related to the tip radius evolution, so the vapor pressure and heat of evaporation can be determined by measuring in situ the radius changes with time. The method permits an easy control of the cleanliness of the surface by field electron microscopy, and should enable one to study the influence of adsorption on evaporation. The method is tested with molybdenum tips. The variation of the radius of the tips, heated in ultra-high vacuum, is determined by field electron and scanning microscope measurements. Vapor pressures and heat of evaporation values obtained are in agreement with values obtained by other techniques.