Crystal-truncation-rod

Great progress has been made, however, in our later study using in situ SXS [Stamenkovic et ak, 2007a], where, by simultaneously fitting the intensity ratio between two different sets of crystal truncation rod (CTR) data that constrain the fit to the full CTR data [Robinson, 1986 Warren, 1990], it was possible to reveal the elemental concentration profile at the surface (Fig. 8.13c). Based on the in situ SXS results depicted in Fig. 8.13a, the topmost surface layer is confirmed to be 100 at%... 

Robinson IK. 1986. Crystal truncation rods and surface roughness. Phys Rev B 33 3830-3836. 

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.)... 

Among the most common surface X-ray scattering techniques used to probe mineral-fluid interface structure is the measurement of crystal truncation rods (CTRs). CTRs are diffuse streaks of intensity connecting bulk reciprocal lattice (Bragg) points in the direction perpendicular to a surface, and arise as a natural... 

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].

In FIGURE 3(a), the signal elongated from (0000) to [OOOn] is called the crystal truncation rod [16-18], which indicates that the film is atomically flat. 

Fig. 8 Illustration of the sapphire (0001) surface truncated bulk and best fit model obtained from crystal truncation rods measurements. The two top planes are strongly shifted with respect to their bulk positions in a nearly bond-length conservative displacement (from Ref. 124).

The MgO(100)-Ni interface was the subject of another SXRD study [59]. Surface preparation replicated that described above and SXRD data were recorded for Ni coverages from 0.2 to 125 ML equivalent. From simulations of the (11 /) crystal truncation rod it was again concluded that part of the Ni film adsorbs on site, and that the epitaxial site is above a surface oxygen. For coverages up to 1 ML equivalent the distance between the MgO surface and... 

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 ... 

Fig. 4 The (01) crystal truncation rod of the Ag(lll)-(V3x /3)R30°-Sb structure. The experimental data points, shown as solid circles, are compared with the results of calculations for optimised versions of the faulted (solid curve) and unfaulted (dashed line) surface alloy models.

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. ... 

Figure 37. Crystal truncation rods (CTRs) for W(IOO) in ultrahigh vacuum. Open circles, experimental data. Solid and dashed lines are, respectively, fits with and without consideration of surface roughness. Inset Reciprocal space diagram. (From Robinson, I. K., Phys. Rev. B. 33, 3830, 1966, with permission.)...

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. 

Figure 41. Crystal truncation rod for a silver(l 11) electrode/solution interface, (a) radial scan, (b) azimuthal (rocking) scan, (c) crystal truncation rod scan. (From Samant, M. G., Toney, M. E., et al., Phys. Rev. B. 38 10962...

Figure 44. Crystal truncation rod for a Pt(l 11) electrode with an iodine monlayer O = ex situ = in situ A = after electrochemical stripping of the iodine monolayer = after electrochemical roughening.

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... 

The crystal truncation rod (CTR). We now calculate the scattering intensity for a semi-infinite lattice, i.e., which has only one reflecting interface. This sum is nearly... 

Crystal truncation rods vs. surface rods. All bulk Bragg points in Figure 6B are intersected by a crystal truncation rod. This is a fundamental property of a terminated lattice (Robinson 1986). The truncation rods are always oriented perpendicular to the physical surface plane, even when the surface plane and the crystallographic plane do not coincide (e.g., a miscut crystal). However, additional surface rods that do not intersect bulk Bragg points are often observed. Such rods would be associated with specific... 

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