Surface x-ray diffraction in combination with scanning tunneling microscopy and molecular dynamics calculations provide first quantitative evidence for unusually large relaxations in nanometer-sized Co islands deposited on Cu(001) at 170 K. These lead to sharply reduced interatomic Co distances as low as 2.36 A as compared to bulk Co (2.51 A) involving low symmetry Co adsorption sites. Our results prove the validity of the concept of mesoscopic mismatch which governs the strain relaxation of nanosized islands in general.

We present a combined surface x-ray diffraction ͑SXRD͒ and theoretical analysis of the geometric structure of nanometer sized Co islands deposited on Cu͑001͒ at 170 K. Two-dimensional nanoislands consisting of only 20-40 atoms are characterized by a 4%-8% contraction of the interatomic distances as compared to the bulk ͑2.51 Å͒. This strongly exceeds "usual" lattice relaxations normally seen for surfaces. The SXRD analysis is based on the analysis of the registry of the Co adatoms relative to the ͑1 ϫ 1͒ surface unit cell of the Cu͑001͒ substrate crystal. Static displacements of the Co atoms of 0.18 Å ͑root mean square͒ out of the equilibrium hollow sites are observed which are in agreement with predictions based on molecular-dynamics calculations.

A highly precise surface x-ray-diffraction study of the uncovered Cu͑001͒ surface kept at 160 K was carried out. Based on two independent experiments we find that the first ͑d 12 ͒ and second ͑d 23 ͒ interlayer spacings are contracted by 1.4Ϯ 0.4% and expanded by 0.3Ϯ 0.4% relative to the bulk value ͑d b = 1.808 Å͒, respectively. The root-mean-square ͑rms͒ isotropic vibrational amplitude of the top layer atoms ͑0.095 Å͒ is enhanced by 80% over the bulk, rapidly decreasing to 20% and 5% for the second and third layers ͑average values͒. The rms amplitude top layer vibrations are isotropic within the experimental uncertainty of about 0.02 Å.The uncovered crystal surface represents one of the most important objects in surface science, since it forms the basis for the study of epitaxial systems. For this reason, the precise knowledge of the structure of clean crystal surfaces is of paramount importance for the understanding of more complex systems in general.In contrast to semiconductor surfaces which often reconstruct, low-index metal surfaces represent seemingly simple substrates. A large number of investigations on the geometric structure of metallic surfaces have been carried out in the past. For an overview we refer to Refs. 1-3. In general, an oscillatory relaxation sequence is observed for the interlayer spacings in which the first interlayer distance ͑d 12 ͒ is contracted by several percent, while the second one ͑d 23 ͒ is expanded.In contrast, the precise analysis of the structural disorder in terms of the thermal atomic vibrations is relatively scarce. This can be attributed to the fact that for many well established k-space analysis tools such as low-energy electron diffraction ͑LEED͒, surface-extended x-ray-absorption fine structure, and photoelectron diffraction, 2,3 the displacement amplitude of the atoms in the near-surface region is not an easily accessible quantity. Thermal vibrations induce only tiny modifications of the scattered intensities and the measurement of very precise intensities is required.At temperatures far below the melting point, thermal disorder can be described in the harmonic approximation using the Debye model leading to the well-known temperature factor T͑q͒ = exp͑−Bq 2 / 4͒. Here, B =8͗u 2 ͘ is the Debye parameter containing the mean-square amplitude of the vibrations ͑͗u 2 ͒͘, and q = ͉q͉ represents the amplitude of the momentum-transfer vector q ͑see Ref. 4͒.In this context, the Cu͑001͒ surface was also a subject of several experimental and theoretical studies; to some of them we refer to Refs. 5-9. For instance, the LEED study by Davis and Noonan 5 provided experimental evidence for the multilayer relaxation. They found a contraction of the first interlayer distance by ⌬d 12 = −1.1% and an expansion of d 23 by ⌬d 23 = + 1.7%. Using spin-polarized LEED experiments, Lind et al. 6 derived ⌬d 12 = −1.2% and ⌬d 23 = + 0.9%.Later, using medium-energy ion scattering ͑MEIS͒ Jiang et al. 7 and Fowler and Barth 8 analyzed the surface layer rootmean-square ͑rms͒ vibration amplitude ͑V 1...

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