Atom-Surface Scattering, Kinematics

11 Compare the contribution to Cv from electrons and phonons at 10 K for copper. Tlie Fermi temperature is 8.2 10 K. At higher temperatures the following expression is obtained for the heat ce acity within the Debye model 

12 Estimate the force constant for a Pt-crystal from the following information on the volume change AV when stretching Pt-thread [116] 

FIGURE 2.11 An atom hits the surface with the incident angle 0, to the surface normal and leaves with the scattering angle f. The surface-projected wavevectors are K/ and Kf. 

By varying the values of the incident energy and angle i, one can cover the full kinematic space according to the following two conservation rules  

Crystal Momentum Conservation The momentum in the parallel plane is conserved to within an reciprocal lattice vector Gnm, i.e., 

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So far, we have treated the intensities - which carry the structural information of the surface - in kinematic approximation, but we have already mentioned that this approximation is by no means valid. This is impressively demonstrated in Figure 3.2.1.17, in which (a) displays the dependence of atomic scattering [/o of a Pt atom (in direct backscattering) together with the kinematic (00)-beam spectrum of Pt(lOO) at normal incidence of the primary beam and normalized with respect to atomic scattering, (same curve as in Figure 3.2.1.11a)). In (b), the same but... 

RHEED is a powerful tool for studying the surface structure of crystalline samples in vacuum. Information on the surface symmetry, atomic-row spacing, and evidence of surfece roughness are contained in the RHEED pattern. The appearance of the RHEED pattern can be understood qualitatively using simple kinematic scattering theory. When used in concert with MBE, a great deal of information on film growth can be obtained. 

RHEED intensities cannot be explained using the kinematic theory. Dynamical scattering models of RHEED intensities are being developed. With them one will be able to obtain positions of the surface atoms within the surface unit cell. At this writing, such modeling has been done primarily for LEED. 

The situation is illustrated in Fig. 3.47. The upper part shows a thin film of Ni deposited on a Si substrate. Only particles scattered from the front surface of the Ni film have an energy given by the kinematic equation, Eq. (3.28), Fi = fCNi o- As particles traverse the solid, they lose energy along the incident path. Particles scattered from a Ni atom at the Si-Ni interface therefore have an energy smaller than On the... 

Fig. 18. Average fractional energy transfer of diretly scattered oxygen atoms as a function of deflection angle, x. for i i) = 47 kJ mol and 6i = 60° (circles). The dashed line is the hard-sphere model prediction based on the effective surface mass, ms, shown. The solid line is the revised prediction after the hard-sphere model is corrected for the internal excitation of the interacting surface fragment. The correction is derived from a kinematic analysis of scattering in the c.m. reference frame.

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