Debye temperature surface

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). 

Figure 5.2 The recoil-free fraction,/, of iron as a function of temperature for different values of the Debye temperature, 6 y Bulk iron compounds have Debye temperatures on the order of 450-500 K surface phases, however, have significantly lower Debye temperatures, implying that measurements may have to be carried out at lower temperatures...

Surface phases have low Debye temperatures. As a result, the recoil-free fraction may be low at room temperature (see Fig. 5.2). Thus, measuring at cryogenic temperatures will increase the Mossbauer intensity of such samples considerably. But there can also be other circumstances which call for low temperature experiments. 

LEED intensities also depend on the lattice vibrations at the surface of the crystal. A high Debye temperature of the surface results in intense LEED spots. In fact, measurement of spot intensities as a function of primary electron energy provides a way to determine the surface Debye temperature [20]. 

In summary, LEED is most often used to verify the structure and quality of single crystal surfaces, to study the structure of ordered adsorbates and to study surface reconstructions. In more sophisticated uses of LEED one also determines exact positions of atoms, the nature of defects and the morphology of steps, as well as Debye temperatures of the surface. 

Vibrations in the surface plane, however, will be rather similar to those in the bulk because the coordination in this plane is complete, at least for fee (111) and (100), hep (001) and bcc (110) surfaces. Thus the Debye temperature of a surface is lower than that of the bulk, because the perpendicular lattice vibrations are softer at the surface. A rule of thumb is that the surface Debye temperature varies between about 1/3 and 2/3 of the bulk value (see Table A.2). Also included in this table is the displacement ratio, the ratio of the mean squared displacements of surface and bulk atoms due to the lattice vibrations [1]. 

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

The fact that the surface Debye temperature is lower than that of the bulk has two consequences. First, the surface is always a weaker scatterer than the bulk. Second, the intensity of the surface signal decreases faster with increasing temperature than the intensity of the bulk signal. Sometimes one can use this property to recognize surface behavior from measurements with bulk sensitive techniques [12]. 

The thermal properties of AU55 are treated in Sect. 3, using especially the results of MES measurements [24,25,42]. These are discussed in connection with the concept of bulk versus surface modes in small particles. An explanation of the temperature dependence of the MES [42] absorption intensities and the Cv results [25] on the basis of a model using the site coordination and the center-of-mass motion are briefly reviewed. The consequences of the Mossbauer results for surface Debye temperatures and for the melting temperature of small gold particles are also discussed. 

The four sites of Aujj exhibit different line intensities, and from the relative site occupations, the Mossbauer f-factors for the different sites could be calculated [24], using standard techniques [91]. These, in turn, could be related to effective Einstein (or Debye) temperatures 0 (or 0 ) associated with the vibrations of the individual sites. An unexpected consequence was that the three surface sites could not be described by a single meaning that the use of... 

The experimental observation that one has different Debye temperatures for the three distinct surface sites of the AU55 cluster makes the use of a continuum-model picture for discussing the thermal behavior questionable. Indeed, for such small particle sizes, where the surface structure is so manifest, the use of the concept of surface modes becomes dubious, and is certainly inadequate to explain the observed temperature dependence of the f-factors. None the less, it has proven possible to describe the low temperature specific heat of AU55 quite well using such a continuum-model, when the center-of-mass motion is taken into account [99],... 

Fig. 4.4. Measured Debye temperatures as a function of electron kinetic energy for Pd top) and Pb bottom) surfaces...

Here D is the depth of the atomic potential as sensed by the incident atom and Mg and Ms are the masses of the scattering atoms and surface atoms, respectively, and 6 is the surface Debye temperature. For the diffracting X-rays and electrons that have much... 

Clearly one obtains the best performance for a given time constant with a detector that has the lowest possible heat capacity. The heat capacity of a crystal varies like C oc (T/0 )3, where On is the Debye temperature. Diamond has the highest Debye temperature of any crystal, so FIRAS used an 8 mm diameter, 25 fim thick disk of diamond as a bolometer (Mather et al., 1993). Diamond is transparent, so a very thin layer of gold was applied to give a surface resistance close to the 377 ohms/square impedance of free space. On the back side of the diamond layer an impedance of 267 ohms/square gives a broadband absorbtion. Chromium was alloyed with the gold to stabilize the layer. The temperature of the bolometer was measured with a small silicon resistance thermometer. Running at T = 1.6 K, the FIRAS bolometers achieved an optical NEP of about 10 14 W/y/IIz. 

Here, is the surface temperature and IF is a Debye-Waller-type factor which is a function of and the effective surface Debye temperature 0 there is currently some discussion as to the most appropriate form for t. 239,240 Atomic- and molecular-beam scattering provides three types of information. 

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