Diffraction spots

LEED angles must be corrected for refraction by the surface potential barrier [73]. Also, the intensity of a diffraction spot is temperature dependent because of the vibration of the surface atoms. As an approximation. 

The relative intensity of a certain LEED diffraction spot is 0.25 at 300 K and 0.050 at 570 K using 390-eV electrons. Calculate the Debye temperature of the crystalline surface (in this case of Ru metal). 

The reciprocal lattices shown in figure B 1.21.3 and figure B 1.21.4 correspond directly to the diffraction patterns observed in FEED experiments each reciprocal-lattice vector produces one and only one diffraction spot on the FEED display. It is very convenient that the hemispherical geometry of the typical FEED screen images the reciprocal lattice without distortion for instance, for the square lattice one observes a simple square array of spots on the FEED display. 

Many fonns of disorder in a surface structure can be recognized in the LEED pattern. The main manifestations of disorder are broadening and streaking of diffraction spots and diffuse intensity between spots [1]. 

Islands occur particularly with adsorbates that aggregate into two-dimensional assemblies on a substrate, leaving bare substrate patches exposed between these islands. Diffraction spots, especially fractional-order spots if the adsorbate fonns a superlattice within these islands, acquire a width that depends inversely on tire average island diameter. If the islands are systematically anisotropic in size, with a long dimension primarily in one surface direction, the diffraction spots are also anisotropic, with a small width in that direction. Knowing the island size and shape gives valuable infonnation regarding the mechanisms of phase transitions, which in turn pemiit one to leam about the adsorbate-adsorbate interactions. 

To obtain spacings between atomic layers and bond lengdis or angles between atoms, it is necessary to measure and analyse the intensity of diffraction spots. This is analogous to measuring the intensity of XRD reflections. 

Because of Bragg s explanation of diffraction of x-rays from a crystal as being like reflections from famihes of planes, the diffraction spots ate usually called "reflections." Each reflection is identified with three integer indices, h, k, and / For the set of planes shown in Figure 7, the indices of the corresponding reflection are /i = 1, = 0, and I = 2. 

The superimposition of diffraction spots from both phases gives the previously reported pattern that was thought to require an eight-chain unit cell. In the la stmcture, because of its one-chain unit cell, all chains must have parallel packing. Since the la and ip stmctures exist in the same microfibril of cellulose, the chains in the ip stmcture should also be parallel. 

The dimensions of the unit cells deduced for Cellulose I seem to depend on the kind of plant that is the source of the cellulose wide ranges are reported (64). Since most Cellulose I s are mixtures of two or more stmctures, with mostiy overlapping diffraction spots, the various observed dimensions could result from different amounts of the la, ip, and possibly other forms. 

Because of the much shorter wavelength of elecuon beams, the Ewald sphere becomes practically planar in elecU on diffraction, and diffraction spots are expected in this case which would only appear in X-ray diffraction if the specimen were rotated. 

In diffraction experiments a narrow and parallel beam of x-rays is taken out from the x-ray source and directed onto the crystal to produce diffracted beams (Figure 18.5a). The primary beam must strike the crystal from many different directions to produce all possible diffraction spots and so the crystal is rotated in the beam during the experiment. Rotating the crystal is much easier than rotating the x-ray source, especially when it is a synchrotron. 

How do we find phase differences between diffracted spots from intensity changes following heavy-metal substitution We first use the intensity differences to deduce the positions of the heavy atoms in the crystal unit cell. Fourier summations of these intensity differences give maps of the vectors between the heavy atoms, the so-called Patterson maps (Figure 18.9). From these vector maps it is relatively easy to deduce the atomic arrangement of the heavy atoms, so long as there are not too many of them. From the positions of the heavy metals in the unit cell, one can calculate the amplitudes and phases of their contribution to the diffracted beams of the protein crystals containing heavy metals. 

Diffraction is usefiil whenever there is a distinct phase relationship between scattering units. The greater the order, the better defined are the diffraction features. For example, the reciprocal lattice of a 3D crystal is a set of points, because three Laue conditions have to be exactly satisfied. The diffraction pattern is a set of sharp spots. If disorder is introduced into the structure, the spots broaden and weaken. Two-dimensional structures give diffraction rods, because only two Laue conditions have to be satisfied. The diffraction pattern is again a set of sharp spots, because the Ewald sphere cuts these rods at precise places. Disorder in the plane broadens the rods and, hence, the diffraction spots in x and y. The existence of streaks, broad spots, and additional diffuse intensity in the pattern is a common... 

When Davisson and Germer reported in 1927 that the elastic scattering of low-energy electrons from well ordered surfaces leads to diffraction spots similar to those observed in X-ray diffraction [2.238-2.240], this was the first experimental proof of the wave nature of electrons. A few years before, in 1923, De Broglie had postulated that electrons have a wavelength, given in A, of ... 

These reciprocal lattice vectors, which have units of and are also parallel to the surface, define the LEED pattern in k-space. Each diffraction spot corresponds to the sum of integer multiples of at and at-... 

Optics) diffraction spot, -gitter, n. diffraction grating, -strahl, m. (Optics) diffraction ray. 

Depending on the size and packing (space group) of the asymmetric unit in the crystal and the resolution available, many tens of thousands of diffraction spots must be recorded to determine a structure. 

The diffraction pattern obtained in the detector plane when the beam scan in a STEM instrument is stopped at a chosen point of the image comes from the illuminated area of the specimen which may be as small as 3X in diameter. In order to form a probe of this diameter it is necessary to illuminate the specimen with a convergent beam. The pattern obtained is then a convergent beam electron diffraction (CBED) pattern in which the central spot and all diffraction spots from a thin crystal are large discs rather than sharp maxima. Such patterns can normally be interpreted only by comparison with patterns calculated for particular postulated distributions of atoms. This has been attempted, as yet, for only a few cases such as on the diffraction study of the planar, nitrogen-rich defects in diamonds (21). 

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