Bernal chart

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A Bernal chart is a simple tool used in crystallography to read X-ray diffraction pictures from a single crystal. It shows where each reflected X-ray spot lies in reciprocal space using cylindrical coordinates: zeta (ζ) along the crystal’s rotation axis, xi (ξ) in the horizontal plane, and phi (φ) the angle between the X-ray beam and the plane containing ζ and ξ. Points with the same ζ lie in a plane perpendicular to the rotation axis, which becomes a layer line on the oscillation photograph; these lines are labeled by ζ (ζ = 0 for the equatorial line, then ζ1, ζ2, etc.). Alternatively, reciprocal points can be pictured on a cylinder with fixed ξ, whose axis is the rotation axis. If the crystal is mounted with the c-axis vertical, the layer spacing H along that axis relates to the detector radius R by H/R = tan μ, where μ is the layer line angle. Reading the contours of constant ζ and ξ helps interpret the rotation photograph. Bernal charts were drawn to show these curves as they appear on an X-ray image, with scale set by the crystal-to-detector distance. Historically, the charts were made as transparencies that could be laid over film to read coordinates directly from the photograph.