Rotation photographs

The first was not the structure of brookite. The second, however, had the same space-group symmetry as brookite (Ft,6), and the predicted dimensions of the unit of structure agreed within 0.5% with those observed. Structure factors calculated for over fifty forms with the use of the predicted values of the nine parameters determining the atomic arrangement accounted satisfactorily for the observed intensities of reflections on rotation photographs. This extensive agreement is so striking as to permit the structure proposed for brookite (shown in Fig. 3) to be accepted with confidence. 

A number of rotation photographs were made with molybdenum. K-radiation filtered through a zirconium oxide filter to isolate the Ka line. The positions of useful reflections, the indices of the planes producing them, and their visually estimated intensities are given in Table V. The factor placed beside the estimated intensity is a correction for the varying time of reflection, namely Vi — (wl/dsin 20)2, where l is the wave-length, and u and d represent respectively the index of the axis of rotation and the unit translation along it1). (A number of reflections... 

It is worthy of mention that the rotation photographs yield information substantiating the choice of FJ as the correct space-group. Thus no reflections occurred from (100), 300, 500, 700, 900, 11-0-0, 13-0-0, 301, 501, 701, 901, 11-0-1, 401, 601, 801, 10 0-1, 12-0-1, etc. on one photograph recorded in Table V, although planes of all these forms were in positions favorable to reflection. Similar failures to reflect were observed on the other photographs. 

We believe that our conclusions can be accepted with considerable certainty, for the agreement between the predicted structure and the experimental results in regard to space-group symmetry, size of the unit of structure, and intensities of reflections on rotation photographs is so striking as to remove nearly completely from consideration the possibility of its being accidental. 

Helvite of unstated origin has also been studied by Gottfried2), who found the value o0 = 8.52 A from rotation photographs. His work also led to the space group T. Neither Barth nor Gottfried suggested an atomic arrangement for the crystal. 

Fig. 3 X-ray diffraction photographs of poly-2,5-DSP. (a) Rotation photograph along the c-axis (oscillation angle 42°) (b) Weissenberg photograph of hkQ zone.

Fig. 8a-c. r rotation photographs of H. marismortui SOS crystals at 0 "C and at cryotemperature (obtained at XI1/EMBL/DESY and at SSRL/Stanford U.) a The hkO-orientation of a nearly perfectly aligned (although split) crystal reveals the mirror symmetry of the C-centred lattice plane. The severe overlap problem in this orientation caused by the large mosaic spread is obvious from this picture, b The Okl-orientation shows the extinctions of the twofold screw axis, c The best crystals have a Bragg resolution limit of about 6 A, which decreases to about 9 A in the course of a hundred exposures... 

The size and shape of the unit cell is determined, usually from rotation photographs and... 

If the spacings of the arcs on a powder photograph do not lead to identification, the determination of unit cell dimensions from the powder photograph may be attempted the methods are described in Chapter VI. If crystals large enough to be handled individually can be picked out of the specimen, single-crystal rotation photographs may be taken and used for identification this also is dealt with in Chapter VI. 

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

Single crystal rotation photographs. Above potassium nitrate (orthorhombic rotation axis, c). Centre gypsum (monoclinic rotation axis, c). Below benzil (hexagonal ... 

Fig. 75. Determination of unit cell dimensions by rotation photographs, (a) for tetragonal, (5) for hexagonal crystals.

Indexing rotation photographs. Preliminary consideration. The spots on the equator of a rotation photograph are obviously reflections from atomic planes which were vertical during the exposure. In Plate VII the equatorial spots are reflections from planes parallel to the c axis, that is, hkO planes the third or l index for these reflections is 0 by inspection. The other two indices, h and k, of all the equatorial reflections may be found from the spacings of the planes, which are worked out from the reflection angles 6 by the Bragg equation. 

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... 

Indexing rotation photographs by reciprocal lattice methods. Orthorhombic crystals. First of all, the coordinates and for each reflection on the photograph (Fig. 86) are found in one of the ways just described these coordinates may be plotted as in Fig. 87 a to form the reciprocal lattice rotation diagram. The problem now is to decide which point of the reciprocal lattice itself corresponds to each spot on the rotation diagram. 

Fig. 86. Coordinates of spots on rotation photograph of orthorhombic crystal.

Oscillation photographs. It often happens that on rotation photographs the positions of two or more possible reflections are so close... 

We wish to find f and y for the spot-corresponding to the reciprocal lattice point P, / is obtained from the distance x of the spot from the centre line of the film (corresponding to the distance along the equator of a fixed-film rotation photograph) if the radius o the cylindrical, r 20... 

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. 

For normal-beam single-crystal rotation photograph, using crystal of volume V completely bathed in X-rays ... 

Zero layer on single-crystal rotation photographs. The spacings d... 

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