X-ray diffuse scattering study of vacancy nanoclusters in homoepitaxial Ag(001) films

Abstract

The analysis of x-ray diffuse scattering measurements on Ag homoepitaxial films is presented. The experiments, which establish that a low concentration of large vacancy clusters can be incorporated into noble metals during homoepitaxial growth, were performed on 100 monolayer films of Ag deposited on Ag(001) at low temperature. The diffuse scattering of this film was measured, in situ, near several in-plane Bragg positions in grazing-incidence geometry. Because of the large dilatation from the vacancy clusters, the usual approximations of Huang and Stokes-Wilson scattering cannot be made and it is shown that numerical integration of the diffuse scattering equations leads to good agreement between the data and a point-defect scattering model.

In-situ x-ray scattering studies of Ag nano-structures

“…Our group performed x-ray diffuse scattering measurements on 100 ML Ag(001) homoepitaxial films, and revealed unexpectedly large local volume dilatation of 750 A 3 and small concentration 0.05% for the average vacancy clusters [52,53], which leads to the vacancy concentration being much less than our previous estimation of 2% for mono-vacancies [50].…”

“…Since a negative volume change is necessary to produce the observed contraction of lattice constant, our group attribute the origin of the substantial compressive strain to a large number of vacancies incorporated in the growing film. The vacancy concentration was originally estimated to be ∼ 2% based on the magnitude of the strain [50] assuming a point defect model and assuming mono-vacancies, although subsequent diffuse x-ray scattering studies [52,53] showed that the strains were gen- erated by a much smaller concentration of large clusters. The 100K-deposited sample was annealed to a higher temperature known for vacancy annealing, and the vacancy concentration indeed disappeared.…”

“…Because the vacancy cluster size is unexpectedly large (about 40 missing atoms), the resulting large displacement field violates assumptions used in the diffuse scattering theories [53]. All the analytical equations to calculate diffuse scattering employed small displacement approximation, which assumed Q • t( r) 1, where Q is the momentum transfer and t( r) is the elastic displacement at a distance r from a point defect.…”

“…When Kim et al [52,53] performed the calculations on 100 ML homoepitaxial films, it was unnecessary to use a thin film model because of the large film thickness. He took the equations for bulk materials from Dederichs [55] and Krivoglaz [56] where no assumption is made about the size of the displacement field, and performed Figure 6.3: Comparison of the measured diffuse scattering intensity (circles) and the numerically calculated intensities (lines) of 100 ML Ag(001) homoepitaxial films.…”

“…Dotted (blue), solid (black), and dashed (red) lines are for vacancy strength -b = 30, 60, and 100, respectively. Reprinted with permission from Kim et al [53]. Copyright 2012 by the American Physical Society.…”