Shear displacement of the K(110) surface

Itchkawitz, B. S.; Baddorf, Arthur P.; Davis, H. L.; Plummer, E. W.

doi:10.1103/physrevlett.68.2488

Cited by 22 publications

(13 citation statements)

References 26 publications

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“…It is well known (see, for instance, Refs. [27,28]) that it is very difficult to distinguish between static and dynamical displacements in LEED analysis, and we believe that Table I carries strong indications that in the actual surface some degree of structural disorder is present, which has erroneously been attributed to dynamical effects. Deviations from clean and flat morphology would certainly affect the apparent rms displacements, the layer relaxations, and their temperature dependence in LEED analysis of "nominally ideal" surfaces.…”

Section: Istituto Nazionale DI Fisica Della Materia (Infm) and Scuolamentioning

confidence: 90%

Ab Initio Study of Be (0001) Surface Thermal Expansion

Lazzeri

Gironcoli

1998

Phys. Rev. Lett.

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We present a first-principles study, within the quasiharmonic approximation, of the thermal expansion of Be (0001) surface. The free energy is obtained from full vibrational dispersions computed by density-functional perturbation theory. Our calculation describes very well the thermal expansion in the bulk and has been checked against first-principles molecular dynamics simulations in the surface case. We do not find the large thermal expansion recently observed experimentally and we argue that the morphology of the actual surface could be less ideal than assumed. [S0031-9007(98) PACS numbers: 63.20. Ry, 68.35.Bs, 71.15.Mb, 82.65.Dp Some metal surfaces displaying anomalously large surface thermal expansion have been recently studied by combining first-principles calculations with a simplified quasiharmonic approximation [1,2]. The validity of such an approach, however, has been criticized by some authors [3] due to the very poor sampling of vibrational modes adopted in the free-energy calculation and needs to be tested against more accurate treatments. Because of its large outward relaxation [4], beryllium (0001) surface has attracted much experimental [4][5][6][7] and theoretical [8][9][10][11][12] interest. Until very recently, there was a substantial disagreement between experimental and first-principles theoretical [8-12] results on the amount of topmost interlayer expansion, theoretical calculations giving roughly half of the observed value. In a recent Letter, Pohl et al.[2] reconcile experiment and theory on this point showing that low temperature (110 K) low-energy electron diffraction (LEED) determinations of the first interlayer separation are in agreement with first-principles (zero temperature, static) calculations and that reported discrepancies at room temperature originate from a large thermal expansion of the top layer, reaching 6.7% at 700 K. These findings are very interesting and puzzling, since surface phonons show no sign of enhanced anharmonicity [2,6]. The calculation of the surface thermal expansion [2], within the simplified quasiharmonic approach of Ref.[1], agrees with experimental findings. However, the accuracy of this approach still needs to be established.In this Letter the thermal expansion of Be (0001) surface is studied from first principles, minimizing the free energy of the surface as a function of the interlayer separation in the quasiharmonic approximation (QHA). The QHA is applied by avoiding additional simplifications [1,2] thanks to the efficient calculation by density-functional perturbation theory [13] of the needed vibrational frequencies. The ability of QHA to deal with thermal effects in bulk solids has been demonstrated in recent studies [14,15]. Here its validity in the more delicate surface case, where larger anharmonicity can take place [16], is explicitly confirmed by comparing it with a first-principles molecular dynamics (MD) simulation at the highest temperature considered (700 K). The approximations involved in the determination of the surface thermal exp...

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Section: Istituto Nazionale DI Fisica Della Materia (Infm) and Scuolamentioning

confidence: 90%

Ab Initio Study of Be (0001) Surface Thermal Expansion

Lazzeri

Gironcoli

1998

Phys. Rev. Lett.

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“…Low energy electron diffraction experiments of the {110} surface revealed the signature of large shears of the surface layer relative the bulk. Electronic structure calculations suggested that force constants governing the shear of the surface layers were so small that zero point motion alone could account for the experimental observations 15,16 .…”

Section: Discussionmentioning

confidence: 99%

Phonons and phase stability in Ti-V approximants to gum metal

et al. 2012

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The stability of competing phases within body-centered-cubic (bcc) Ti-V approximants to Gum Metal is considered from the perspective of the phonon dispersion. Phonons are associated with the potential to form the ω and α ′′ phases. It is argued that alloys can be designed to be linearly stable with respect to the formation of both phases, even as the ideal shear strength approaches zero. The reduction in ideal strength is associated with softening of the phonons along Γ − N , and is reflected in diffuse scattering diffraction experiments.

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“…Such an in situ growth of alkali-metal single crystals provides a unique opportunity to prepare well ordered and clean surfaces of these fundamentally interesting metals. 6,7 More recently, helium atom scattering ͑HAS͒ was applied to investigate the growth of Na films deposited on Cu͑001͒ ͑Ref. 8͒ and of Na, Rb, and Cs films on a graphite surface.…”

Section: Introductionmentioning

confidence: 99%

Strain and confined resonances in ultrathin alkali-metal films

Hulpke¹,

Lower²,

Reichmuth

1996

Phys. Rev. B

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We have investigated the structure and lattice dynamics of ultra-thin alkali-metal films in the systems K/Ni͑001͒ and Cs/Cu͑111͒ using the technique of high-resolution helium atom scattering ͑HAS͒. Our results are compared with those from an earlier HAS study of Na/Cu͑001͒. For all of these systems, lattice mismatch at the substrate/film interface introduces strain in the films which is found to be gradually removed during the growth process. Our comparative study shows that relaxation of the alkali-metal films into the bulk alkali metal occurs more rapidly as one proceeds from Na to K and Cs. The presence of strain relief is revealed in our observations of a layer-dependent Debye-Waller effect, the Debye temperature in the film decreasing with increasing film thickness from values close to that of the substrate to the bulk alkali-metal Debye temperature. More detailed information on strain relief in the alkali-metal films is provided by the variations in their vibrational frequencies with increasing film thickness. As for the Na/Cu͑001͒ system, the K and Cs films investigated here exhibit prominent confined vibrational resonances. Our results show that measurements of the vibrations of atoms in the film surface yield information not only on the force constants at the film surface but also on those within the film itself. Comparison of results between the different alkali-metal systems elucidates further the nature of the growth process, the development of strain relief during growth, and the behavior of confined vibrational resonances.

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Shear displacement of the K(110) surface

Cited by 22 publications

References 26 publications

Ab Initio Study of Be (0001) Surface Thermal Expansion

Ab Initio Study of Be (0001) Surface Thermal Expansion

Phonons and phase stability in Ti-V approximants to gum metal

Strain and confined resonances in ultrathin alkali-metal films

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