Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 4.5, pp. 481-482   | 1 | 2 |

Section Crystallization and data collection

D. L. Dorsetb* Crystallization and data collection

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The success of electron crystallographic determinations relies on the possibility of collecting data from thin single microcrystals. These can be grown by several methods, including self-seeding, epitaxic orientation, in situ polymerization on a substrate, in a Langmuir–Blodgett layer, in situ polymerization within a thin layer and polymerization in dilute solution. If these preparations do not provide sufficient information, then data can also be collected from microfibres. Thin cast films have also been examined after stretching.

Self-seeding (Blundell et al., 1966[link]) has been one of the most important techniques for growing single chain-folded lamellae. The technique is very simple. A dilute suspension of the polymer is made in a poor solvent. The temperature is raised to cause total solubilization of the macromolecule and then lowered to room temperature to crystallize ill-formed particles (mostly dendrites). The temperature is then elevated again until the suspension just clears, leaving small seeds of the polymer crystals behind. Upon lowering to a suitable temperature above ambience, which is then fixed, isothermal crystallization of well formed lamellae is allowed to occur over time. When the crystallization procedure is complete, the suspension can be cooled again to room temperature and the lamellae harvested. These lamellae are typically less than 10 nm thick, with lateral dimensions between 1.0 and 10.0 µm.

Epitaxic orientation techniques, to give alternative projections of the chain packing, have become increasingly important in recent years. While inorganic substrates have been described (Mauritz et al., 1978[link]), the use of organic layers for this purpose (Wittmann & Lotz, 1990[link]; Lotz & Wittmann, 1993[link]) has been more promising because these substrates are less easily contaminated by adsorbed gases and water vapour, and because the nucleation is anisotropic. Often the crystallization can be carried out from a cooled co-melt, i.e. a dilute solution of the polymer in the organic small molecule. When the liquidus curve of the eutectic phase diagram is crossed, the diluent crystals form first. Since these have a surface lattice spacing closely resembling that of the polymer-chain packing, the polymer chains can be directed to lie along the substrate surface, rather than normal to it, as the solidus line of the phase diagram is crossed. The substrate can then be removed by some suitable technique (sublimation, selective solvation) to permit the investigation of the oriented film. Variations of this procedure include crystallization of polymer-chain segments from the vapour phase onto a substrate (Wittmann & Lotz, 1985[link]) and in situ crystallization of monomers that have first been epitaxically oriented on a suitable substrate (Rickert et al., 1979[link]).

A number of other possibilities for crystal growth also exist. Langmuir troughs have been used to orient monomers that may have hydrophilic moieties. If the monomers contain triple bonds that can be cross-linked, then a polymer film can be formed, e.g., if the condensed monomer film is exposed to ultraviolet light (Day & Lando, 1980[link]). It may be possible to carry out the polymerization within a confined space (Rybnikar et al., 1994[link]) or in dilute solution (Liu & Geil, 1993[link]) to form crystals suitable for electron diffraction data collection. In the latter case, whisker formation with the chain axis parallel to the lath plane has been observed. Films can be cast on a water surface by evaporation of an organic solvent from a polymer solution. The film can then be stretched to give a suitably oriented specimen for data collection (Vainshtein & Tatarinova, 1967[link]). In addition, it may just be possible to obtain suitable data from drawn microfibres to supplement the single-crystal diffraction information from other preparations.

Data collection from these thin microcrystals often employs the selected-area diffraction technique in the electron microscope that is described in detail elsewhere (Dorset, 1995b[link]). Using an approximately eucentric goniometric tilting device in the electron microscope, the sampling of three-dimensional reciprocal space is tomographic, i.e. the tilts of a nearly planar Ewald sphere surface (owing to the very small electron wavelength) are always referred to a set of reciprocal axes that intersect (0, 0, 0). For any given crystal habit, there is always a missing set of data owing to the physical limitation to the tilt imposed by the finite thickness of the specimen holder within the pole-piece gap of the electron microscope objective lens (Vainshtein, 1964[link]). For this reason, it is desirable to crystallize two orthogonal orientations of the chain packing (using the above-mentioned approaches), if possible, so that all of the reciprocal lattice can be sampled. If electron micrographs are to be used as an additional source of crystallographic phases then `low-dose' techniques for recording such images should be employed to reduce the deleterious effects of radiation damage caused by the inelastic interactions of the electron beam with the crystalline sample (Tsuji, 1989[link]).

When the diffraction patterns are recorded on photographic film and these are then measured with a densitometer, relative reflection intensities can often be expressed simply as the integrated peak area without need for a Lorentz correction (Dorset, 1995b[link]). Only if the diffraction maxima are extensively arced (e.g. in patterns from epitaxic films) is such a correction required. That is to say, [|\Phi_{\rm obs}| \propto KI_{\rm obs}^{1/2}] where [|\Phi_{\rm obs}|] is the observed structure-factor magnitude. Assuming the kinematical approximation holds, the calculated value is [\Phi_{h}^{\rm calc} = {\textstyle\sum\limits_{i}}\; f_{i} \exp 2\pi i ({\bf h} \cdot {\bf r}), ] where [f_{i}] are the electron scattering factors (Doyle & Turner, 1968[link]), e.g. as tabulated in Table[link] in IT C. By analogy with X-ray crystallography (see Chapter 2.2[link] ), normalized values can be found from [|E_{h}|^{2} = I_{h}^{\rm obs} / \varepsilon {\textstyle\sum\limits_{i}}\; f_{i}^{2},] with the usual scaling condition that [\langle E_{h}^{2}\rangle = 1.000]. [Note, however, that these intensities only describe the chain monomer packing in the `stem' region of the lamellar microcrystal. Details owing to the surface chain folds are lost (even if they are strictly periodic), because of reasons similar to those described by Cowley (1961)[link] for the electron scattering from elastically bent silicate crystals.]


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