Cylindrical films

X-ray powder diffraction studies are perfonned both with films and with counter diffractometers. The powder photograph was developed by P Debye and P Scherrer and, independently, by A W Hull. The Debye-Scherrer camera has a cylindrical specimen surrounded by a cylindrical film. In another commonly used powder... 

Fig. 74. Arrangements for taking single-crystal rotation photographs (a) on flat films, (6) on cylindrical films.

The length of c can be obtained very simply from this photograph by measuring the distance y of any layer line from the equator if the camera radius is r, then rjy is tan c is then given by wA/ccs , n being the number of the layer line selected (the equator having n = 0). For the potassium nitrate crystal, c is G-45 A. If a flat film is used instead of a cylindrical film, the layer lines are shown, not as straight lines... 

When the reflections are recorded on a cylindrical film the height y of each layer of spots above the equator is rcot< , where r is the radius of the cylinder. 

Fig. 83. Sphere of reflection surrounded by cylindrical film of unit radius, a. Elevation. b. Plan.

Bernal (1926) worked out and for all positions on a cylindrical film, and gave a chart (illustrated in Fig. 84). Transparent charts of this type, suitable for a cylindrical film 6 cm in diameter, can be obtained from the Institute of Physics (47 Belgrave Square, London, S.W. 1) it is only necessary to place a rotation photograph on the chart, and read off the and coordinates for every spot on the film. Similar charts for flat films (specimen to film distance 4 cm) can also be obtained. Greater accuracy is obtained by measuring the positions of... 

Fig. 84. Bernal chart giving f and J for positions on cylindrical film. (Bernal, 1926.)... 

We have, first of all (Fig. 85 a), the primary beam passing through the crystal at right angles to its axis of rotation and striking the cylindrical film (radius r) at the point X. Erect the axis XC parallel to the... 

When diffracted X-ray beams fall on a photographic film at different angles, as the different layer lines in a cylindrical-film rotation photograph do, it is necessary to correct for the absorption of X-rays in different thicknesses of film. (Since double-coated films are normally used, the effect on the back layer depends on the absorption in the film.) This was first considered by Cox and Shaw (1930) Whittaker (1953) gives a formula which is more accurate and deals with greater obliquity and a thicker film Grenville-Wells (1955) gives the corrections when the multiple film method is used. 

It will be assumed here that the X-ray diffraction data were collected on flat films with a point focus camera. This simplifies the theoretical presentation. The TMV data analyzed in the results section were collected on cylindrical films with Guinier cameras, but positions on the cylindrical films can be mapped onto positions on a flat film by a simple geometric transformation. In general, the form of the optical density, D(r,), in a fiber diffraction pattern can be expressed in film coordinates as the sum of contributions from all reflections, I (r,iJ> ), plus a background term, B(r,) ... 

The distance along the abscissa measures the angle characteristic of reflection from a given set of crystal planes. The diagram on the left side of the figure indicates schematically how the cones of reflected radiation intersect the cylindrical film in the camera before it is removed for analysis. The actual analysis of the pattern obtained in this manner can be made in the usual manner (Barrett, 110) and will not be described here. 

Layer lines When a crystal is rotated or oscillated about a principal axis, the diffraction spots on a cylindrical film surrounding the crystal are arranged in a series of straight lines called layer lines. These layer lines are perpendicular to the axis of rotation. 

For the case of a cylindrical film or IP where the axis of the cylinder is coincident with the rotation axis (figure A1.2(c)) then, for T in degrees, ... 

The most powerful method that can be used to determine unknown crystal structures is the rotating crystal technique. In this method a single crystal of good quality (of at least 0.1 mm in the smallest dimension) is mounted with one of its axes normal to a monochromatic beam of x-rays and rotated about in a particular direction. The crystal is surrounded by cylindrical film with the axis of the film being the same as the axis of rotation of the crystal. By repeating this process of rotation in a number of directions, the rotating crystal method can be used to determine an unknown crystal structure. 

The size of the cations in PPy acmators was found to be a cracial factor, with a faster response given for smaller cations for cylindrical films formed in Nap-TS, showing that the bending mechanism was controlled by cation insertion and extraction [107]. For PPy films doped with [Fe(CN)e], a larger deformation was estabhshed with increased solvation of the alkali-metal cation used, in the order Li > Na > K [122]. This finding was confirmed in a further study using PPy(DBS) tubular films [104]. 

Figure 5 2. The Debye-Scherrer powder method. An X-ray R passes through a collimator and then meets a powder preparation P. The reflections caused by P lie on cones of reflection, which form crescents or arcs on a cylindrical film F.

Fig. 49. Diffraction phenomenon in a linear point lattice taken on a cylindrical film parallel layer lines are produced.

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