X-ray diffraction in liquids

These calculations are extremely tedious fortunately, they can be done by computer. But even before the advent of high-speed computers, the structures of hundreds of crystals had been worked out by hand calculation. The fruits of these x-ray studies are seen in the structures described earlier in this chapter. 

The diffraction pattern of a liquid resembles a powder photograph except that the very sharp lines of the powder photograph are replaced by a few broad bands of reflected radiation. From an analysis of the intensity distribution in these broad bands, we can construct the radial distribution function for particles around a central particle in the liquid. This distribution function is interpreted in terms of the average number of atoms surrounding a central atom at the distance corresponding to the peak. 

1 Contrast the bonding and structure in (a) metals and (b) ionic crystals. 

2 Ionic crystals are quite brittle and easily cleave when struck. Explain this by considering the electrostatic forces generated when two layers in the crystal are displaced. 

3 Diamond is one of the hardest substances known. Account for this in terms of its structure. 

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Krishnamurti, P. X-ray diffraction in liquid mixtures. Proc. Indian Assoc. Cultiv. Sci. 12 (1929) 331-355. 

Stewart, G. W. and Skinner, E. W. (1928). X-Ray diffraction in liquids A comparison of certain primary normal alcohols and their isomers. Phys. Rev., 31,1-9. 

The purpose of this chapter is to review ultrafast, time-resolved X-ray diffraction from liquids. Both experimental and theoretical problems will be treated. The stmcture of the chapter is as follows. Section II describes the principles of a time-resolved X-ray experiment and details some of its characteristics. Basic elements of the theory are discussed briefly in Sections III-V. Finally, Section VI presents recent achievements in this domain. The related field of time-resolved X-ray spectroscopy, although very promising, wiU not be discussed. 

The purpose of this section is to describe recent achievements in time-resolved X-ray diffraction from liquids. Keeping the scope of the present chapter in mind, neither X-ray diffraction from solids nor X-ray absorption will be discussed. The majority of experiments realized up to now were performed using optical excitation, although some recent attempts using infrared excitation were also reported. The main topics that have been studied are (1) visualization of atomic motions during a chemical reaction, (2) structure of reaction intermediates in a complex reaction sequence, (3) heat propagation in impulsively heated liquids, and (4) chemical hydrodynamics of nanoparticle suspensions. We hope that the actual state-of-the-art will be illustrated in this way. 

We have used x-ray diffraction in our laboratory to probe transient structures of laser-excited liquids, small-molecule crystals and protein crystals. The diffraction patterns are recorded on a CCD detector that makes efficient use of most of the diffracted x-rays. Several experimental protocols have been developed Laue diffraction from proteins [6-8], small-molecule diffraction [9,10] and diffraction from liquids [2,11,12]. In proteins, the... 

The structure of liquids can be analyzed by the calculated radial distribution function (RDF), which defines the solvation shells. In Fig. 16.1, the calculated RDF of the liquid Aris shown, and in Table 16.1, the structure is compared with the experimental results. Four solvation shells are well defined. The spherical integration of these peaks defines the coordination number, or the number of atoms in each solvation shell. The first shell that starts at 3.20A has a maximum at 3.75A, and ends at 5.35 A, has an average of 13 Ar atoms. Therefore, in the first solvation shell, there is a reference Ar atom surrounded by other neighboring 13 Ar atoms. All the maxima of the RDF, shown in Table 16.1, are in good agreement with the experimental results obtained by Eisenstein and Gingrich [29], using X-ray diffraction in the liquid Ar in the same condition of temperature and pressure. The calculated... 

Table 16.1 Comparison of the calculated structure of liquid Argon with the experimental data obtained by X-ray diffraction in the same thermodynamic condition (T = 91.8 K and P = 1.8 atm)...

Pershan PS, Als-Nielsen J (1984) Phys Rev Lett 52 759 Als-Nielsen J (1986) Solid and liquid surfaces studied by synchrotron X-ray diffraction. In Blanckenhagen W (ed) Structure and dynamics of surfaces. Springer, NY... 

Fontell, K. (1974) X-ray diffraction by liquid crystals- amphiphilic systems. In G.W. Gray and P.A. Winsor (eds), Liquid Crystals and Plastic Crystals. Ellis Horwood Publishers, Chichester,... 

The radial distribution function, g(r), can be determined experimentally from X-ray diffraction patterns. Liquids scatter X-rays so that the scattered X-ray intensity is a function of angle, which shows broad maximum peaks, in contrast to the sharp maximum peaks obtained from solids. Then, g(r) can be extracted from these diffuse diffraction patterns. In Equation (273) there is an enhanced probability due to g(r) > 1 for the first shell around the specified molecule at r = o, and a minimum probability, g(r) < 1 between the first and the second shells at r = 1.5cr. Other maximum probabilities are seen at r = 2(7, r = 3 o, and so on. Since there is a lack of long-range order in liquids, g(r) approaches 1, as r approaches infinity. For a liquid that obeys the Lennard-Jones attraction-repulsion equation (Equation (97) in Section 2.7.3), a maximum value of g(r) = 3 is found for a distance of r = <7. If r < cr, then g(r) rapidly goes to zero, as a result of intermolecular Pauli repulsion. 

There have been excellent reviews on X-ray diffraction in studying structures of low- and high mass liquid crystals (e.g., Wendorff, 1978 ... 

Variation of proton disorder with temperature in carboxyl dimers has been observed by Kanters, Roelofsen and Kroon [88] in the crystal structure of monofluoromalonic acid, using X-ray diffraction. At liquid nitrogen temperature the carboxyl group is ordered, but at room temperature the protons are disordered. Direct evidence for dynamic double proton exchange in carboxyl dimers was demonstrated by solid state NMR studies in />-toluic acid [89] and benzoic acid [90]. For the / -toluic acid dimer, Ernst and coworkers deduced an asymmetric double minimum potential 19 with an energy difference AG = 0.24kcalmol and an activation energy = 1.14 kcal mol between the two tautomers. At room temperature... 

Seddon, J.M., 1998. Structural studies of Uquid crystals by X-ray diffraction. In Demus, D., Goodby, J.W., Gray, G.W., Spiess, H.-W., Vill, V. (Eds.), Handbook of Liquid Crystals. Volume 1 Fundamentals. Wiley-VCH, Weinheim, p. 635. 

In the foregoing sections we have discussed the molecular arrangement in crystals and liquids and can appreciate how greatly the use of x-ray diffraction in this field has increased our knowledge it remains now to show that the interference method is capable of a wider application which has proved very useful in colloid chemistry and particularly so in the domain of high polymers. 

Fig. 5.1 A set-up for a study of X-ray diffraction on liquid crystals X-ray tube (X), beam collimators (C), mirrors (M), a detector (D) and a data acquisition system (PC). A sample is represented by a stack of parallel layers placed in a camera with controllable temperature installed between the poles of a magnet...

X-ray diffraction has been the most usefitl technique in investigating the microscopic structure of liquid crystals. X-ray diffraction from liquid crystals is just like Bragg scattering from crystals, in that periodicities in the structure of the phase give rise to constructive interference and therefore peaks in the scattering of X-rays. 

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