Crystal truncation rod diffraction

Figure 7.3. (a) In situ X-ray reflectivity vs. time (measured at the anti-Bragg condition, shown in inset at top) during dissolution of orthoclase feldspar, KAlSi308, (001) cleavage surface at extreme pH values. The removal of successive monolayers (ML) is noted for each set of data, (after [100]) (b) in situ crystal truncation rod diffraction profiles for a freshly cleaved orthoclase (001) surface (circles) and after reaction at pH = 2.0 (1 and 15 ML dissolved) (diamond and square) and pH = 12.9 (2 ML dissolved) (triangle) (after [103]). (Figures provided by P. Fenter.)... 

Trainor TP, Eng P, Brown GE Jr, Robinson IK, De Santis M (2002b) Crystal truncation rod diffraction study of the clean and hydrated a-Al203 (1-102) surface. Surf Sci 496 238-250 Trainor TP, Eng P, Brown GE Jr, Wayuchunas GA, Newville M, Sutton S, Rivers M (2002d) Crystal truncation rod diffraction study of the hydrated a-Fe203 (0001) surface. 2001 Activity Report, Advanced Photon Source... 

Figure 7.15. (A) Crystal truncation rods along the (00L), (10L), (11L), and (20L) zones, showing results of modeling [38] (B) Best-fit model for the a-Al203 (0001)/water interface [38] (C) CTR diffraction data for the UHV clean a-Al203 (0001) surface [168] (D) Best-fit model of the UHV-clean a-Al203 (0001) surface showing that the surface is terminated by A1 atoms [168].

Consider now a perfect crystal truncated by a sharp surface (or semi-infinite crystal). It can be obtained by the product of a step function describing the electron density variation perpendicular to the surface, and an infinite lattice. The diffraction pattern is then the convolution of the 3D reciprocal lattice with the Fourier transform of the step function. An infinity of Fourier components is necessary to build this latter, so that there remains non zero intensity in between Bragg peaks as a function of / the reciprocal space is made of rods of intensity, called crystal truncation rods (CTR), extending perpendicular to the surface, and connecting bulk Bragg peaks [24, 25]. The intensity variation as a function of (or Qj or /) is found by stopping the summation at n3 = 0 in Eq. (1) and (2), yielding ... 

As mentioned previously, a crystal will diffract x-rays with an intensity proportional to the square of the structure factor and is described by Eq. (33). The abrupt termination of the lattice at a sharp boundary (i.e., a surface) causes two-dimensional diffraction features termed crystal truncation rods (CTRs). Measurements of CTRs can provide a wealth of information on surface roughness and may be useful in the determination of crystallographic phase information. ... 

In the case of thin films or monolayers, two different techniques can be employed these are the total external-reflection Bragg diffraction (TERBD) technique introduced by Eisenberger and Marra and the previously mentioned technique based on crystal truncation rods, introduced by Robinson, which can provide in-plane structural information or information on interfacial roughness, respectively. 

Theory It is beyond the scope of this review article to provide a comprehensive description of basic X-ray diffraction from surfaces. Instead, readers are referred to the excellent reviews by Fei-denhans l [1], Fuoss and Brennan [2], and Robinson and Tweet [3] for explicit details. In this section, we will focus on some basic ideas that pertain to X-ray diffraction studies of surfaces in an electrochemical environment, in particular with regard to crystal-truncation rod (CTR) measurements. 

Figure 3.4.2 The amplitude along a crystal truncation rod, assuming the amplitude of a single unit cell to be equal to 1. Bulk Bragg peaks occur for integer values of the diffraction index /. The amplitude at these...

Figure 3A2.5 Real and reciprocal space of a crystal with a flat top surface. Reciprocal space consists of crystal truncation rods, that is, diffraction rods in which the strong bulk Bragg peaks are connected by weak tails of diffuse intensity. The specular rod, or (00) rod, has no in-plane momentum transfer.

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