Three problems in surface physics: surface thermal expansion, surface screening, and metal-vacuum tunneling

Abstract

Several fundamental problems in the area of surface solid state physics have been investigated: first , we have calculated the coefficients of thermal expansion for the first two interplanar spacings near the (111) and (100) surfaces of Ar, Kr, and Xe. The bulk thermal expansion, which is obtained as a by-product in the calculation, is found to be in good agreement with experimental measurements at all temperatures up to the melting point (largely because of the cancellation of errors at higher temperatures). This fa c t provides some confidence in the method and in the results for the surface thermal expansion. At high temperatures, the results for the surface thermal expansion are in agreement with the prediction of an approximate model which we gave earlier, ??[subscript surface]/??[subscript bulk] = (3/4)<u[superscript 2][subscript z]>[subscript surface]/<u[superscript 2][subscript z]>[subscript bulk]. At low temperatures, ??[subscript surface]/??[subscript bulk] passes through a rather high peak (with a value of greater than 6 for the (100) surface) because of dispersion of the surface modes. We are unable to give a conclusive explanation of the large apparent discrepancy between our calculations and the experimental observations of Ignatiev and Rhodin, which if taken at face value indicate that ??[subscript surface]/??[subscript bulk] is greater than twice our result for the (111) surface of Xe between 55??K and 75??K. However, it is possible that factors other than thermal expansion influence the shifts in the Bragg peaks which are observed experimentally, as has been found to be the case in other attempts to measure surface thermal expansion. A nonkinematical calculation of temperature effects in LEED from Xe(111) would be of interest in this regard, and also in regard to apparent discrepancies between theoretical and experimental "effective Debye temperatures" at the lowest energies. Experimental observation of the strong peak in ??[subscript surface]/??[subscript bulk] would also be of interest; this peak occurs at roughly 6% of the bulk Debye temperature and therefore should be observable in metals or other materials at cryogenic temperatures. ...