Thermal motion, relative mean squared

Figure 3. Comparison of relative mean squared thermal motion for bulk and surface Ft atoms as a function of temperature. The triangles mark the catalyst surface atoms, the circles are for bulk Ft.

Atoms taking part in diffusive transport perform more or less random thermal motions superposed on a drift resulting from field forces (V//,-, Vrj VT, etc.). Since these forces are small on the atomic length scale, kinetic parameters established under equilibrium conditions (i.e., vanishing forces) can be used to describe the atomic drift and transport, The movements of atomic particles under equilibrium conditions are Brownian motions. We can measure them by mean square displacements of tagged atoms (often radioactive isotopes) which are chemically identical but different in mass. If this difference is relatively small, the kinetic behavior is... 

Photoionization (and therefore EXAFS) takes place on a time scale that is very short relative to atomic motions, so the experiment samples an average configuration of the neighbors around the absorber. Thus, one needs to consider the effects of thermal vibration and static disorder, both of which will have the effect of reducing the EXAFS amplitude. These effects are considered in the so-called Debye-Waller factor which represents the mean-square relative displacement along the absorber-backscatterer direction and is given by... 

Incidentally, this happens to be the most cited paper by Einstein - more than relativity and more than ever3dhing else. The physics of why the temperature T appears in Equation (12.11) is quite clear. For given values of /X and t, the mean-square displacement (12.10) must increase with growing temperature, that is when the thermal motion becomes more intense. 

The values of below the critical temperature, derived from the areas of the spectra, are associated with the local thermal motions of the individual iron atoms relative to their neighbours. The. total mean square displacements of the iron atoms above 7, derived from the areas of the narrow subspectra, were resolved into three components associated with different modes of thermal motions ., s and fc corresponding to local, slow collective and fast collective modes, respectively. This is shown in Figure 6.17 for metmyoglobin and ferritin. The value of ,o,. is obtained by a linear extrapolation from the values of below the critical temperature. The difference between and ioc gives the mean-square collective displacement associated with large-scale motions of parts of the surrounding protein and is resolved into the two parts and fc. The values of correspond to slow... 

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