Multilayer Relaxation

Numerical calculations and dilfraction optimizations also suggest coexistence of bond contraction and expansion extending to deeper atomic layers for a number of metals [44], Multilayer relaxation happens to Ag(410) and Cu(320) surfaces [45]. The multilayer relaxation is subject to the data processing iteration. The same set of Ag(410) LEED database gives rise different conclusions. One is non-measur-able relaxation and the other is a 36 % contraction of the d2i and a 18 % expansion of 34 [46]. Theoretical calculations clarified this discrepancy with a 11.6, 5.3, and 9.9 % contraction of the Ag(410) outermost three interlayer separations and followed by 2.1 and 6.7 % expansion subsequently. A combination of LEED, DPT, and MD [47] investigation turned out that the di2 of Ag(l 10) surface contracts by 8 % at 133 K and by 0.2 % at 673 K associated with a rise in the Debye temperature from 150 65 to 170 100 K compared with the bulk value of 225 K. 

For a Cu(320) surface, a 13.6 and 9.2 % contraction of the first two interlayers are followed by an expansion of 2.9 %, and then an 8.8 % contraction, and finally a 10.7 % expansion for the subsequent three [45]. The di2 of the Au(llO) surface is reduced by 13.8 %, the d2% is expanded by 6.9 %, and finally the 34 is reduced by 3.2 % [48]. On the other hand, LEED measurements of Cu(320) revealed a 24 % contraction for d 2 and 16 % contraction for d i, followed by 10 % expansion for 34. Therefore, physical constraints are necessary to specify a unique solution from these derived by mathematically geometrical optimizations. 

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The BFS method has been applied to a variety of problems, ranging from the determination of bulk properties of solid solution fee and bee alloys and the defeet strueture in ordered bee alloys [28] to more speeifie applieations ineluding detailed studies of the strueture and eomposition of alloy surfaees [29], ternary [30] and quaternary alloy surfaees and bulk alloys [31,32], and even the determination of the phase strueture of a 5-element alloy [33]. Previous appheations have foeused on fundamental features in monatomie [26] and alloy surfaces [29] surface energies, reconstructions, surface structure and surface segregation in binary and higher order alloys [34,35] and multilayer relaxations [36,37]. While most of the work deals with metallic systems, the lack of restrictions on the type of system that can be studied translated into the extension of BFS to the study of semiconductors [38]. 

Seyller Th, Diehl RD, Jona F (1999) Low-energy electron diffraction study of the multilayer relaxation of Cu(211). J Vacuum SciTechnA 17 1635-1638... 

Geng WT, Kim M, Freeman AJ (2001) Multilayer relaxation and magnetism of a high-index transition metal surface Fe(310). Phys Rev B 63 245401... 

Geng WT, Freeman AJ, Wu RQ (2001) Magnetism at high-index transition-metal surfaces and the effect of metalloid impurities Ni (210). Phys Rev B 63 064427 Zhang X-G, Van Hove MA, Somorjai GA et al (1991) Efficient determination of multilayer relaxation in the Pt(210) stepped and densely kinked surface. Phys Rev Lett 67 1298—1301 Hartel S, Vogt J, Weiss H (2010) Relaxation and thermal vibrations at the NaF(lOO) surface. Surf Sci 604 1996-2001... 

In subsequent studies relying as well on the FLAPW approach "" the effects of multilayer relaxation on the reconstruction of the W(OOl) surface were investigated. Surface reconstruction effects were found for the topmost four atomic layers with the theoretical results being within the range of the experimental error bar for the top two layers. Experiments are not sensitive enough to allow conclusions for the relaxations of the deeper layers whereas computations still show small relaxations for the third and fourth layer beneath the surface. 

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