Extending the rule of mixture to the sub unit-cell level

An extension of the rule of mixture (ROM) to the sub unit-cell level is reported. This approach—which was tested for MAX and MnAl4C3+n phases—provides a reliable estimate of the bulk moduli of single phases with layered crystal structure based on the calculated moduli of the constituents. Based on the ROM, density functional theory combinatorics is developed, reducing the calculation time for elastic properties by some orders of magnitude. This is a significant step towards knowledge-based materials design since elastic properties can be predicted based on an efficient high-throughput methodology.