Corrugation inversion

In this section, we discuss the effect of tip states. Those tip states will create inverted images, where the sites of surface atoms are minima rather than maxima in the topographic images (Barth et al. 1990). 

The general expression for the tunneling current can be obtained using the explicit forms of tunneling matrix elements listed in Table 3.2. To put the five d states on an equal footing, normalized spherical harmonics, as listed in Appendix A, are used. The wavefunctions and the tunneling matrix elements are listed in Table 5.1. 

The first term in Eq. (5.58) represents the uncorrugated tunneling current, which decays much more slowly than the corrugated terms. Therefore, if Do is not too small, the corrugation of the topographic image is 

The enhancement factor E, that is, the quantity in the parenthesis in this equation, is displayed in Fig. 5.10. Because the corrugation amplitude depends only on the relative intensities of different components, we normalize it through 

Naturally, the results can be represented by a diagram similar to a three-component phase diagram, as shown in Fig. 5.10. Several interesting features are worth noting. First, when the m = 0 or state dominates, a large, positive enhancement is expected. The condition for a substantial enhancement is quite broad. For example, when the condition 1.21 Di -i- 0.21D21 is satis- 

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The corrugation inversion due to tip states is a universal phenomenon in the STM imaging of low-Miller-index metal surfaces. For most metals (except several alkali and alkaline earth metals, which have rarely been imaged by STM), the nearest-neighbor atomic distance a 3 A. Consequently, the numerical coefficients on Eq. (5.61) are very close to those for Au(lll). 

Corrugation inversion (continued) quantitative interpretation 141 Coupling constants 220 Curie point 218 Current amplifiers 251—258 frequency response 254 microphone effect 256 picoarameter 251, 252 Current images 121 Cu(lll) 18... 

Tip-state effects 19—20, 126, 297 atomic resolution, and 32 corrugation enhancement 125 corrugation inversion, and 137 graphite, and 146 layered materials, on 20 metal surfaces, on 19 scanning tunneling spectroscopy, and 24, 308 Tip-sample distance 53... 

The MEL framework type is closely related to MFI. The corrugated sheets of pentasil chains that are found in MFI are also present in the MEL framework [Figure 2.33(a)], However, in MEL, the adjacent sheets are related to one another by a mirror plane instead of an inversion center as in MFI. This produces straight 10-ring channels along both x- and y-directions with a free aperture of 5.4 x 5.3 A [Figure 2.33(b)],... 

Fig. 10. The MFI framework type with pentasil chains running parallel to z. One corrugated sheet perpendicular to z has been highlighted in gray. Adjacent sheets are related to one another by inversion centers (in the 6- and 10-rings).

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