Metal surface Debye temperature

Surface phonon bands along symmetry lines of the SBZ are given for fee metals in Figs. 5.2-49-5.2-55 and in Table 5.2-20. In all figures the horizontal axis is the reduced wave vector, expressed as the ratio to its value at the zone boundary. Table 5.2-21 gives the surface Debye temperatures for some fee and bcc metals, as well as the amplitudes of thermal vibrations of atoms in the first layer p as compared with those of the bulk pb-In the harmonic approximation, the root mean square displacement of the atoms is proportional to the inverse of the Debye temperature. 

Table 5.2-21 Surface Debye temperatures of metals. References to the original articles are given in [2.4,6] ...

Table 5.2-21 Surface Debye temperatures of metals, cont.

The relative intensity of a certain LEED diffraction spot is 0.25 at 300 K and 0.050 at 570 K using 390-eV electrons. Calculate the Debye temperature of the crystalline surface (in this case of Ru metal). 

Table A.2 Ratio of surface and bulk displacements, and Debye temperatures of several metals f 1],...

TABLE 4.1. Surface and Bulk Root-Mean-Square Displacement Ratios and Debye Temperature for Several Metals... 

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. 

In this equation v is a phonon frequency, such that hv is approximately k, with the Debye characteristic temperature of the metal. The quantity p is the product of the density of electrons in energy at the Fermi surface, N(0), and the electron-phonon interaction energy, V. 

Debye-Waller factors from the bulk metal for the interstitial sites. The disorder for the surface sites was larger over the whole temperature range. 

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