Effect of stacking faults on diffraction: The structure of lithium metal

A new method for calculating the effect of stacking faults on x-ray and neutron-diffraction patterns is developed. Using a computer-generated, statistically faulted crystal model, we show that it is possible to examine the effect of various types of faults in different lattice types from a simple and unified point of view. As a benchmark on the application of this method, we recover the standard results obtained by approximate analytical techniques for deformation and growth faults in face-centered-cubic lattices. We then use this method to analyze stacking faults in the 9R hexagonal lattice. A detailed comparison of these calculations with our neutron powder-diffraction results on the low-temperature martensitically transformed phase of lithium metal is given. We find that the structure of Li at 20 K is 9R with a deformation stacking-fault probability density of 0.07 per layer. Finally, we show how this method can be extended to more complex stacking-fault types and other crystal structures.