Meyerheim, Holger L.; Moritz, Wolfgang; Schulz, H.; Eng, P. J.; Robinson, Ian K.
Anharmonic thermal vibrations observed by surface X-ray diffraction for Cs Cu(001).
In: Surface Science, Vol. 331-333, No. PART B: pp. 1422-1429
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Surface X-ray diffraction measurements at 190 and 303 K have been used to analyse the thermal disorder of an uniaxial incommensurate quasi-hexagonal Cs-monolayer on Cu(001). Within the harmonic vibration model a Debye-like thermal behaviour is found for the mean square vibration amplitudes Uii (i = 1,2) of the Cs-atoms along the  (i = 1) and the  (i = 2) direction, where the adsorbate structure is commensurate and incommensurate with the substrate, respectively. At 190 K we determine U11 = 0.10(2) A ̊2 and U22 = 0.16(2) A ̊2, at 303 K U11 = 0.18(2) A ̊2 and U22 = 0.29(3) A ̊2. From this temperature dependence Debye temperatures of θ = 45 K and θ = 35 K are derived which are comparable with the bulk Cs-Debye temperature of 38 K. A significant better agreement between calculated and observed structure factors is obtained by taking account of anharmonic contributions to the thermal disorder using the Gram-Charlier series expansion of the harmonic (Gaussian) probability density function. Besides a larger width of the probability density function along  and  the derived anharmonic probability density function exhibits a stronger anisotropy as compared to its harmonic counterpart. The shape of the anharmonic probability density function can directly be correlated to the geometry of the Cs-overlayer structure. At 190 K this is most evident by a small width of the anharmonic probability density along , where the Cs-atoms are arranged in a densely packed chain. At 303 K the anisotropy is less pronounced indicating isotropisation close to the break down of the structure at 328 K.