Bernal chart

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

A Bernal chart for a cylindrical camera of any radius may be constructed graphically by drawing the plan and elevation of this model. Thus, if the height of any reciprocal lattice point above the origin is r and its distance from the axis of rotation is r(, the position of the reflection on the film is obtained in the following way. Draw a circle of radius r (Fig. 85 e), and then a chord NUT at a distance r from the centre (this is the circle of contact seen edgewise) UT is the radius of the circle of contact for this reciprocal lattice point. Join OT and produce to W on the line XC which is parallel to OU. WX is then the ordinate y of the spot on the film. Now draw the plan, that is, draw another circle of radius r (Fig. 85/ ) and in it describe a circle of radius UT. On this circle NT mark off the points Pv P2 which are at a distance r from X, and produce UPX to Yx and UP2 to Y2. The arcs XJ and XY2 are the abscissae x of the two reflections on the film produced by this plane. By doing this for a number of different values of r and rg, the complete chart is obtained. 

Bernal chart, 209 Bernal, John D., 209 Bernard, Claude, 135 Bernoulli, Daniel, 135 Berthollet, Claude-L., 135,192,... 

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... 

Assuming that the equatorial reflections have been shown to fit a rectangular reciprocal lattice net, attention may be turned to the upper and lower layer lines. The values for all the spots are read off on Bernal s chart, and the reciprocal lattice rotation diagram is constructed from these values if the values for the upper and lower layer lines correspond with those of the equator—that is, row7 lines as well as layer lines are exhibited as in Fig. 80—then the unit cell must be orthorhombic. It should be noted that some spots may be missing from the equator, and it may be necessary to halve one or both of the reciprocal axes previously found to satisfy the equatorial reflections. The dimensions of the unit cell, and the indices of all the spots, follow immediately from the reciprocal lattice diagrams. 

Fig. 12.52 Two forms of Ihe [CutNOjJJ1- ion. All bond distances in angstroms. (From Klandcrman. K. A Hamilton, W. C. Bernal. I. Ittorg. Chart. Acta 1977. 2J. 117-129 Reproduced with permission.]...

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