Algorithm for generating derivative structures

We present an algorithm for generating all derivative superstructures--for\narbitrary parent structures and for any number of atom types. This algorithm\nenumerates superlattices and atomic configurations in a geometry-independent\nway. The key concept is to use the quotient group associated with each\nsuperlattice to determine all unique atomic configurations. The run time of the\nalgorithm scales linearly with the number of unique structures found. We show\nseveral applications demonstrating how the algorithm can be used in materials\ndesign problems. We predict an altogether new crystal structure in Cd-Pt and\nPd-Pt, and several new ground states in Pd-rich and Pt-rich binary systems.\n