Thermal expansion of the Ag(111) surface measured by x-ray scattering

Abstract

We have investigated the structure of the Ag͑111͒ surface, for temperatures between 300 and 1100 K ͑90% of the bulk melting point͒, using synchrotron x-ray diffraction. Our data show no evidence of the anomalously large surface thermal expansion previously reported by medium-energy ion-scattering ͓Phys. Rev. Lett. 72, 3574 ͑1994͔͒. At all temperatures we find that the interlayer separations at the surface differ from their bulk counterparts by less than 1%, indicating that the surface expands similarly to the underlying bulk crystal. This behavior is in good agreement with results from molecular dynamics simulations. DOI: 10.1103/PhysRevB.63.113404 PACS number͑s͒: 68.35.Ja, 61.10.Kw, 68.35.Bs As the temperature of a metal is raised toward its bulk melting point, the separations between the atomic layers at the surface can expand considerably faster than the ones in the bulk. This behavior, first observed on Pb͑110͒, 1 is believed to originate from an enhanced anharmonicity of the surface vibrations, whose other manifestations include roughening and surface premelting.2 Subsequent experiments have also revealed an enhanced surface thermal expansion, although somewhat smaller in magnitude, for a number of other low Miller-index metallic surfaces.3-5 However, extensive efforts to quantitatively explain these experimental results have not led to a consensus on a correct theoretical description. 6-10Recently, a medium-energy ion-scattering ͑MEIS͒ study of Ag͑111͒ 3 reported an unexpectedly large high-temperature surface thermal expansion, where the relaxation of the first interlayer spacing, ⌬ 12 ϭ͓(d 12 Ϫd)/d͔, was observed to increase from Ϫ2.5%, its value at temperatures between 300 and 670 K, to ϩ10% at Tϭ1100 K. Here, d 12 is the separation between the first and the second atomic layers at the surface and d is the interlayer spacing in the bulk crystal. Such dramatic structural changes, unanticipated for the close-packed ͑111͒ surface, 11 have attracted considerable theoretical interest. Molecular dynamics ͑MD͒ simulations 7,8 and quasiharmonic approximation ͑QHA͒ calculations 9,10 have been used to investigate the thermal expansion of Ag͑111͒ but, surprisingly, the two methods yielded substantially different results. While the former ͑MD͒ indicates that the surface expands almost bulk-like at all temperatures between 200 K and 1200 K, in apparent contradiction to the MEIS experiment, the latter ͑QHA͒ predicts a large hightemperature surface thermal expansion, somewhat resembling the experimental findings. However, neither the magnitude nor the temperature dependence of the top interlayer relaxation observed in the MEIS experiment was accurately described by the QHA studies. Furthermore, it has been suggested 12 that the QHA method overestimates the surface thermal expansion, particularly at high temperatures.In order to clarify the thermal expansion of Ag͑111͒, we have studied this surface for temperatures between 300 and 1100 K using x-ray reflectivity, which is a technique that is well known for its abili...

Comparative study of anharmonicity: Ni(111), Cu(111), and Ag(111)

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Molecular structure and vibrations of NTCDA monolayers on Ag(111) from density-functional theory and infrared absorption spectroscopy

“…The four-layer slab model employed here (two bottom layers fixed) gives the correct relaxation sign and magnitude for the change of the first (Dd 12 /d b = À0.9%) and the second interlayer spacing (Dd 23 /d b = À0.3%) relative to the bulk spacing (d b ), when compared to LEED 62 and X-ray scattering studies. 63 Note that the LEED study showed that the third interlayer spacing is the same as the bulk interlayer spacing thus legitimating our four-layer slab approach. More refined results would need the consideration of finitetemperature effects which have been discussed in the past but are not the aim of this study.…”

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