Algorithm for sorting diffraction data from a sample consisting of several crystals enclosed in a sample environment apparatus

A sample environment apparatus, such as a diamond-anvil cell (DAC), cryostat or furnace, presents a unique problem for the crystallographer because some of the diffraction data are shadowed by its components. The first algorithm for sorting diffraction data from a sample consisting of several crystals enclosed in a sample environment apparatus is described. This algorithm requires no previous knowledge of the crystal structure of the sample, so it can be used to solve the structures of substances when the growth of one unstrained crystal is unsuccessful. An example is given to illustrate the development and the implementation of this algorithm: the identification of the unit cell of a high-pressure phase of oxygen known as epsilon-oxygen ([epsilon]-O₂). The [epsilon]-O₂ sample contains at least seven individual crystals and is enclosed in a DAC. The [epsilon]-O₂ unit cell is monoclinic, it contains eight molecules per unit cell and the lattice constants at 19.7 GPa and room temperature are a = 3.642, b = 5.491, c = 7.705 Å and β = 116.2°. In the example, monochromatic X-ray diffraction data from this high-pressure sample are sorted, but the algorithm is a general-purpose technique; it can also be used to sort single-crystal time-of-flight neutron diffraction data. Additionally, this method may be used to sort reflections from several crystal samples containing a mixture of materials. The algorithm is given in symbolic logic so that it can be translated and inserted into available crystallographic software packages.