Layer spacing relaxation

Surface type and surface Surface structure, including bond length [and layer spacing] relaxations, relative to bulk Method References Comments... 

C (lll)-H (diamond) (lxl) Hydrogen terminated diamond, sur- MEIS/2/ face layer spacing relaxed by -0.05 0.05 A. 

There are relaxations in the layer registries for the stepped iron (211) and (210) surfaces in addition to layer spacing relaxations. 

Hydrogen-terminated diamond surface layer spacing relaxed by -0.05 0.05 A. 

Most metal surfaces have the same atomic structure as in the bulk, except that the interlayer spaciugs of the outenuost few atomic layers differ from the bulk values. In other words, entire atomic layers are shifted as a whole in a direction perpendicular to the surface. This is called relaxation, and it can be either inward or outward. Relaxation is usually reported as a percentage of the value of the bulk interlayer spacing. Relaxation does not affect the two-dimensional surface unit cell synuuetry, so surfaces that are purely relaxed have (1 x 1) synuuetry. 

In many materials, the relaxations between the layers oscillate. For example, if the first-to-second layer spacing is reduced by a few percent, the second-to-third layer spacing would be increased, but by a smaller amount, as illustrated in figure Al,7,31b). These oscillatory relaxations have been measured with FEED [4, 5] and ion scattering [6, 7] to extend to at least the fifth atomic layer into the material. The oscillatory nature of the relaxations results from oscillations in the electron density perpendicular to the surface, which are called Eriedel oscillations [8]. The Eriedel oscillations arise from Eenni-Dirac statistics and impart oscillatory forces to the ion cores. 

The atomic structure of a surface is usually not a simple tennination of the bulk structure. A classification exists based on the relation of surface to bulk stnicture. A bulk truncated surface has a structure identical to that of the bulk. A relaxed surface has the synnnetry of the bulk stnicture but different interatomic spacings. With respect to the first and second layers, lateral relaxation refers to shifts in layer registry and vertical relaxation refers to shifts in layer spacings. A reconstructed surface has a synnnetry different from that of the bulk synnnetry. The methods of stnictural analysis will be delineated below. 

Figure 5 Summary plot of the transition temperatures (lower), inverse of the smectic layer spacing (middle), and temperature of the a relaxation (upper) of polybibenzoates as a function of the number of methylene units in the spacer Ti, [Ref. 9] T, , [Ref. 9] A I/d, [Ref. 7] T T , [Ref. 9] open symbols our results.

Layer compound cleaved between two 3-plane layers top contraction by —1.6% [-4.7%], first Van der Waals spacing contracted [-3%] Fluorite structure terminated between two Na layers no relaxation as MoSj(OOOl), but top contraction by —0.2% [-0.6%], first Van der Waals spacing contracted [—1.4%]... 

Where relaxation of the metal layer spacing has been investigated this is listed in the table after the adsorbate information.)... 

NbSe2 (0001) (layer compound) (1x1) Normal layer stacking with Se-Nb-Se termination, no evidence for relaxation of first two layer spacings. LEED/13/... 

ZnO (1120) (wurtzite) (lxl) Terminated bulk structure, no evidence for reconstruction or relaxation in layer spacings. LEED/20/... 

Below room temperature, the W(100)c(2x2) reconstructed surface is created by lateral movements of the W atoms in first W layer which propagate into at least the second layer of the surface (fig. 3). Alternate atoms move along the (Oil) direction to form zig-zag chains. A LEED structural study (Pendry et al., 1988) determines the amplitude of the lateral movements to be 0.24 0.04 A in the top W layer and 0.028 0.007 A in the second W layer. The top layer relaxes into the surface by -7.0 2.0% of the bulk interlayer spacing, the second layer spacing expands by +1.2 2.0%. These structural parameters are in reasonable agreement with a recent X-Ray diffraction (XRD) determination (Altmann et al., 1988) which finds that the amplitude of the lateral movements is 0.24 0.05 A in the top W layer and 0.10 0.05 A in the second W layer. By XRD, the top layer is found to relax into the surface by -4.0 1.0% of the bulk interlayer spacing. 

The determination of Si(lll)(l xl) structure produced by laser-annealing the Si(lll)(7x7) remains inconclusive. A detailed LEED study (Jones and Holland, 1985) found two candidate structures. In both structures, the surface atom sinks into the surface whilst the second layer spacing is expanded. In the first candidate structure, the top layer spacing contracts by 0.2 A from its bulk terminated value of 0.78 A, whilst the second layer spacing increases by 0.1 A from its bulk value of 2.35 A. The second structure comprises of much more extensive relaxations in which the top layer spacing contracts by 0.70 0.02 A whilst the second layer spacing increases by 0.6 A This produces an almost graphitic surface in which the separation between the top two Si planes is less than 0.05 A. 

Figure 6. (A) A terminated crystal having surface lattice spacings, a and b, and layer spacing c along the surface normal direction. (B) The reciprocal-space structure for the structure in (A) note that every Bragg peak is intersected by a CTR. (C) Side view of the surface in (A) whose surface symmetry has been modified by adsorption resulting in a doubling of the unit cell dimension, 2a, and by a subsequent lateral surface relaxation in the outermost substrate layer. (D). A reciprocal space schematic of the surface in (C). The doubling of the surface unit cell results in new surface rods at Qx = n a, 3 / ...(shown as vertical dashed lines) that do not intersect any bulk Bragg peaks.

Terminated bulk diamond no relaxation in layer spacing. 

Normal layer stacking with Se-Nb-Se termination no evidence for relaxation of first two layer spacings. 

Recently, Ag(lll) in 0.1 M KOH was also studied by SXS [46], and, as in the previous study, the surface was characterized by measurement of the non-specular CTRs and specular CTR. In alkaline solution there is no competition between OH and anions for adsorption sites, and the SXS data can be interpreted purely on the basis of the surface coverage by OHaa. At -0.95 V (vs SCE) the best fit parameters to the CTR data indicated that the surface layer undergoes a small inward relaxation (contraction) of 0.8% of the Ag(lll) layer spacing... 

The magnitude of the relaxations derived from the best fit are as follows 0.35 A expansion in the topmost layer (25% of the layer spacing), an inward displacement of 0.08 A in the second layer (6%), a buckling of 0.08 A in the third layer, and root-mean-square roughness of 0.41 and 0.16 A in the first and second layers, respectively (the bulk thermal roughness is 0.05 A). The relaxation directions are indicated in the schematic model of the structure in Fig. 9. 

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