Bibliothek

Notizen: Diffusivities have for the first time been quantitatively measured for two-dimensional clusters of iridium atoms on a metal surface, Ir(111). As cluster size increases from two to seven atoms, the diffusivity generally diminishes, but tetramers are an exception. It is shown that their high mobility comes about because of weak interatomic binding, and a low activation energy for diffusion, rather than from a change in the mechanism of motion, which involves displacements of individual adatoms independent of cluster size.

Notizen: Measurements with the field ion microscope have been made of the distribution function governing the displacements of a single metal atom diffusing on W(211). It is shown that by comparing such measurements with the predictions of random walk models, the contributions of jumps of different lengths to the overall diffusion can be ascertained, even if diffusion is dominated by transitions between adjacent sites. Extensive observations for rhenium, as well as for molybdenum atoms on W(211) are best represented by a symmetric random walk between nearest-neighbor sites, without any contribution from longer jumps. For iridium and rhodium atoms, however, double jumps do appear to participate in the diffusion, but amount to only ≈3% of the total.

Notizen: If activated chemisorption occurs directly from the gas phase and also from a precursor state on the surface, then the importance of internal molecular excitations as compared with translational motion in promoting chemisorption can be determined by rate measurements under two different conditions: (a) When the surface and the gas are kept isothermal, the net activation energy is the same whether translational or internal motions contribute to activation, and is given by the difference Ec−Ed between the barrier Ec to the conversion of the precursor into the chemisorbed state and the barrier Ed to the desorption of the precursor back into the gas phase. (b) When the surface is kept cold and only the gas is heated, the activation energy for chemisorption directly from the gas phase is measured. The result will be equal to that in (a) only if the translational energy of the incident molecules can be utilized effectively in passing over the barrier. If internal motions must be excited, however, a higher activation energy, approaching in value Ec , will be measured in experiments with the gas heated. A special apparatus has been built for doing adsorption studies of the type (b), on freshly evaporated metal films maintained at a temperature different from that of the surrounding gas. Measurements of chemisorption on rhodium films at 0 °C, with CH4 at temmperatures from 35 to 91 °C, yield an activation energy of 11.1 kcal/mol, as compared with a value of 5.0 kcal/mol determined in previous isothermal experiments. The difference between the activation energies found for CH4 in experiments of type (a) and type (b) is in excellent agreement with the desorption energy Ed of precursor molecules established previously. This is expected if internal molecular motions, such as vibrations, rather than translation are most effective in promoting the passage of methane over the barrier to chemisorption.

Notizen: Diffusion on bcc (110) of dimers made up of two chemically different atoms is examined for a model in which motion occurs by transitions from a ground state, in which two atoms are in nearest-neighbor sites along 〈111〉, to an intermediate state with the atoms in adjacent sites along either 〈100〉 (horizontal) or 〈110〉 (vertical transition). In this representation, diffusion can be viewed as a random walk of the center of positions (COP) of the dimer atoms over a plane grid of stable and intermediate sites. Starting from the Kolmogoroff equation, a detailed stochastic analysis is carried out for horizontal transitions. This yields the mean-square displacement in terms of four elementary jump processes of the dimer; in addition, the moment generatingfunction and higher moments of the dimer displacements along the Cartesian coordinates x and y are also obtained. These quantities are found to differ for the two axes quite apart from differences in length scales: relaxation to the long-time limits occurs at different rates. For systems in which the population of dimers in the intermediate state is negligible, only the rates a and c at which the two different dimer atoms jump to the intermediate state affect the moments significantly; however, these rates are not separately accessible from observations of the mean-square displacement. The probability distribution for dimer displacements over (110) is therefore worked out explicitly. Displacements are referenced to coordinate axes χ and η along the close-packed 〈111〉 direction, along which COP motion is assumed tooccur. On this χ–η grid, the dimer executes a novel random walk, in which transitions from one axis to another are allowed only at intermediate-state positions; at ground-state positions, motion is restricted to one dimension. For short diffusion intervals, the probability distribution is found to be sensitively dependent on the jump rates a and c. The asymmetry of the distribution of displacements about 〈100〉 provides an immediate qualitative indication of any difference in the rates at which the chemically different dimer atoms jump out of the stable configuration. The actual value of these rates can be obtained from a quantitative comparison with experimentally measured distributions. Dimer diffusion involving vertical transitions, through an intermediate oriented along 〈110〉, is also considered, but more briefly. It is shown that the sum of the two rate constants for jumps into thisintermediate can be derived from observations of the rate at which flips occur from one orientation to another. The mean-square displacement under steady-state conditions is demonstrated to have the same general form as for horizontal transitions alone, but with an additional term for the effective jump rate out of the ground state via this new channel. Finally, the general formalism is adapted to the diffusion of simple dimers, of chemically identical atoms, both on bcc (110) and (100). For simple dimers which are not found in the intermediate state to any perceptible extent, a single jump rate suffices to define the mean-square displacement as well as the distance distribution function.