Ray Diffraction Patterns

Jamieson J C, Lawson A W and Nachtreib N D 1959 New device for obtaining X-ray diffraction patterns from substances exposed to high pressures Rev. Sc/, instrum. 30 1016... 

Idistribution functions can be measured experimentally using X-ray diffraction. The regular arrangement of the atoms in a crystal gives the characteristic X-ray diffraction pattern with bright, sharp spots. For liquids, the diffraction pattern has regions of high and low intensity but no sharp spots. The X-ray diffraction pattern can be analysed to calculate an experimental distribution function, which can then be compared with that obtained from the simulation. 

Gelatin stmctures have been studied with the aid of an electron microscope (23). The stmcture of the gel is a combination of fine and coarse interchain networks the ratio depends on the temperature during the polymer-polymer and polymer-solvent interaction lea ding to bond formation. The rigidity of the gel is approximately proportional to the square of the gelatin concentration. Crystallites, indicated by x-ray diffraction pattern, are beUeved to be at the junctions of the polypeptide chains (24). 

Fig. 1. Structures of (O) atoms and corresponding electron and x-ray diffraction patterns for (a) a periodic arrangement exhibiting translational symmetry where the bright dots and sharp peaks prove the periodic symmetry of the atoms by satisfying the Bragg condition, and (b) in a metallic glass where the atoms are nonperiodic and have no translational symmetry. The result of this stmcture is that the diffraction is diffuse.

Figure 1 shows the decomposition sequence for several hydrous precursors and indicates approximate temperatures at which the activated forms occur (1). As activation temperature is increased, the crystal stmctures become more ordered as can be seen by the x-ray diffraction patterns of Figure 2 (2). The similarity of these patterns combined with subtie effects of precursor crystal size, trace impurities, and details of sample preparation have led to some confusion in the Hterature (3). The crystal stmctures of the activated aluminas have, however, been well-documented by x-ray diffraction (4) and by nmr techniques (5).

Stmctural order varies from x-ray indifferent (amorphous) to some degree of crystallinity. The latter product has been named pseudoboehmite or gelatinous boehmite. Its x-ray diffraction pattern shows broad bands that coincide with the strong reflections of the weU-crystallized boehmite. 

Nordstrandite. Tlie x-ray diffraction pattern of an aluininum tiiliydroxide wliich differed from the patterns of gibbsite and bayerite was pubhshed (4) prior to the material, named nordstrandite, being found in nature. Tlie nordstrandite structure is also assumed to consist of double layers of hydroxyl ions and aluininum occupies two-tliirds of the octaliedral interstices. Two double layers are stacked with gibbsite sequence followed by two double layers in bayerite sequence. 

Several nonequilihrium forms of aluminum oxides have been observed (11,12) in hydrothermal experiments at low water vapor pressures in the temperature region of 300—500°C. The KI—AI2O2 form, also known as tondite [12043-15-1] AI2O2 I/5H2O, is characterized by a distinct x-ray diffraction pattern. 

Fig. 5. X-ray diffraction pattern of commercial samples (a) coUoidal silica, DuPont Ludox TM50 (b) silica gel, Sylodent 700 (c) precipitated silica, PPG...

For a two-dimensional array of equally spaced holes the difftaction pattern is a two-dimensional array of spots. The intensity between the spots is very small. The crystal is a three-dimensional lattice of unit cells. The third dimension of the x-ray diffraction pattern is obtained by rotating the crystal about some direction different from the incident beam. For each small angle of rotation, a two-dimensional difftaction pattern is obtained. 

In principle, it is possible to calculate the detailed three-dimensional electron density distribution in a unit cell from the three-dimensional x-ray diffraction pattern. 

The stmcture of activated carbon is best described as a twisted network of defective carbon layer planes, cross-linked by aHphatic bridging groups (6). X-ray diffraction patterns of activated carbon reveal that it is nongraphitic, remaining amorphous because the randomly cross-linked network inhibits reordering of the stmcture even when heated to 3000°C (7). This property of activated carbon contributes to its most unique feature, namely, the highly developed and accessible internal pore stmcture. The surface area, dimensions, and distribution of the pores depend on the precursor and on the conditions of carbonization and activation. Pore sizes are classified (8) by the International Union of Pure and AppHed Chemistry (lUPAC) as micropores (pore width <2 nm), mesopores (pore width 2—50 nm), and macropores (pore width >50 nm) (see Adsorption). 

Crystal Structure. Diamonds prepared by the direct conversion of well-crystallized graphite, at pressures of about 13 GPa (130 kbar), show certain unusual reflections in the x-ray diffraction patterns (25). They could be explained by assuming a hexagonal diamond stmcture (related to wurtzite) with a = 0.252 and c = 0.412 nm, space group P63 /mmc — Dgj with four atoms per unit cell. The calculated density would be 3.51 g/cm, the same as for ordinary cubic diamond, and the distances between nearest neighbor carbon atoms would be the same in both hexagonal and cubic diamond, 0.154 nm. 

Eig. 1. Laue x-ray diffraction pattern of a single natural graphite crystal. 

Zeolites and Catalytic Cracking. The best-understood metal oxide catalysts are zeoHtes, ie, crystalline aluminosihcates (77—79). The zeoHtes are well understood because they have much more nearly uniform compositions and stmctures than amorphous metal oxides such as siUca and alumina. Here the usage of amorphous refers to results of x-ray diffraction experiments the crystaUites of a metal oxide such as y-Al202 that constitute the microparticles are usually so small that sharp x-ray diffraction patterns are not measured consequendy the soHds are said to be x-ray amorphous or simply amorphous. 

X-ray diffraction patterns yield typical 1.2—1.4 nm basal spacings for smectite partially hydrated in an ordinary laboratory atmosphere. Solvating smectite in ethylene glycol expands the spacing to 1.7 nm, and beating to 550°C collapses it to 1.0 nm. Certain micaceous clay minerals from which part of the metallic interlayer cations of the smectites has been stripped or degraded, and replaced by expand similarly. Treatment with strong solutions of... 

A 1.0 nm basal spacing exhibited in a diffractogram peak that is somewhat broad and diffuse and skewed toward wider spacings characterizes the x-ray diffraction pattern of iUite. Polymorphs may be present (120). Muscovite derivatives are typicaUy dioctahedral phlogopite derivatives are trioctabedral. 

The index of refraction of allophane ranges from below 1.470 to over 1.510, with a modal value about 1.485. The lack of characteristic lines given by crystals in x-ray diffraction patterns and the gradual loss of water during heating confirm the amorphous character of allophane. Allophane has been found most abundantly in soils and altered volcanic ash (101,164,165). It usually occurs in spherical form but has also been observed in fibers. 

The hydrated alumina minerals usually occur in ooUtic stmctures (small spherical to eUipsoidal bodies the size of BB shot, about 2 mm in diameter) and also in larger and smaller stmctures. They impart harshness and resist fusion or fuse with difficulty in sodium carbonate, and may be suspected if the raw clay analyzes at more than 40% AI2O2. Optical properties are radically different from those of common clay minerals, and x-ray diffraction patterns and differential thermal analysis curves are distinctive. 

Clays are composed of extremely fine particles of clay minerals which are layer-type aluminum siUcates containing stmctural hydroxyl groups. In some clays, iron or magnesium substitutes for aluminum in the lattice, and alkahes and alkaline earths may be essential constituents in others. Clays may also contain varying amounts of nonclay minerals such as quart2 [14808-60-7] calcite [13397-26-7] feldspar [68476-25-5] and pyrite [1309-36-0]. Clay particles generally give well-defined x-ray diffraction patterns from which the mineral composition can readily be deterrnined. 

Mica [12001 -26-2]—Cl Pigment White 20, Cl No. 77019. A white powder obtained from the naturally occurring mineral muscovite mica, consisting predominantly of a potassium aluminum siHcate, [1327-44-2] H2KAl2(Si0 2- Mica may be identified and semiquantitatively determined by its characteristic x-ray diffraction pattern and by its optical properties. 

Figure 12.12 X-ray diffraction pattern from crystals of a membrane-bound protein, the bacterial photosynthetic reaction center. (Courtesy of H. Michel.)...

TEM offers two methods of specimen observation, diffraction mode and image mode. In diffraction mode, an electron diffraction pattern is obtained on the fluorescent screen, originating from the sample area illuminated by the electron beam. The diffraction pattern is entirely equivalent to an X-ray diffraction pattern a single crystal will produce a spot pattern on the screen, a polycrystal will produce a powder or ring pattern (assuming the illuminated area includes a sufficient quantity of crystallites), and a glassy or amorphous material will produce a series of diffuse halos. 

Scherrer equation to estimate the size of organized regions Imperfections in the crystal, such as particle size, strains, faults, etc, affect the X-ray diffraction pattern. The effect of particle size on the diffraction pattern is one of the simplest cases and the first treatment of particle size broadening was made by Scherrer in 1918 [16]. A more exact derivation by Warren showed that. 

Fig. 6. The X-ray diffraction patterns and calculated best fits from the structure refinement program for the samples MCMB2300, iVICMB2600 and iVfCMB2800.

Fig. 9. Powder X-ray diffraction pattern for the (002) peak of CRO pitch samples as indicated. The data sets have been offset sequentially by 0, 500, 2000, 4400 and 5400 counts for clarity...

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