Miller indices demonstration

In summary, a Pd(l 1 1) single-crystal surface is not sufficient to model the complex adsorption behavior of palladium nanoparticles, even for nanoparticles which mostly exhibit (111) facets. High Miller index stepped or kinked single-crystal surfaces may provide better models of nanoparticles. However, one should remember that CO adsorbed on defects of defect-rich Pd(l 11) became invisible at high coverages Furthermore, it will be demonstrated in a following section that the... 

Abstract Enantioselective heterogeneous catalysis requires surfaces with structures that are chiral at the atomic level. It is possible to obtain naturally chiral surfaces from crystalline inorganic materials with chiral bulk structures. It is also possible to create naturally chiral surfaces from achiral materials by exposing surfaces that have atomic stractures with no mirror symmetry planes oriented perpendicular to the surface. Over the past decade there have been a number of experimental and theoretical demonstrations of the enantiospecific physical phenomena and surface chemistry that arise from the adsorption of chiral organic compounds on the naturally chiral, high Miller index places of metals. 

In this crystal lattice system, all surfaces with Miller indices, (hkl), satisfying the conditions h x k x 1 and h k l h are chiral [11]. Although such high Miller index surfaces have been studied for decades, it was not until recently that McFadden et al. specifically pointed out and demonstrated that their low synunetry structures render them chiral and, therefore, that they might have enantiospecific interactions with chiral adsorbates [12]. There has been a growing interest in the enantiospecific properties of naturally chiral metal surfaces and in the possibility of using such surfaces for enantioselective chemical processes. 

Any reciprocal lattice vector, or reciprocal lattice point is uniquely specified by the set of three integers, hkl, which are the Miller indexes of the family of planes it represents in the crystal. Thus there is a one-to-one correspondence between reciprocal lattice points and families of planes in a crystal. It will be seen shortly that the reciprocal lattice is the Fourier transform of the real lattice, and vice versa. This was in fact demonstrated experimentally in Figure 1.7 of Chapter 1 by optical diffraction. As such, reciprocal space is intimately related to the distribution of diffracted rays and the positions at which they can be observed. Reciprocal space, in a sense, is the coordinate system of diffraction space. 

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