Chemical Pressure Schemes for the Prediction of Soft Phonon Modes: A Chemist's Guide to the Vibrations of Solid State Materials

The vibrational modes of inorganic materials play a central role in determining their properties, as is illustrated by the importance of phonon electron coupling in superconductivity, phonon scattering in thermoelectric materials, and soft phonon modes in structural phase transitions. However, the prediction and control of these vibrations requires an understanding of how crystal structure and the stiffness of interatomic interactions are related. For compounds whose relationships between bonding and structure remain unclear, the elucidation of such structure property relationships is immensely challenging. In this Article, we demonstrate how the Chemical Pressure (CP) approach can be used to draw-visual and intuitive schemes relating the structure and vibrational properties of a solid state compound using the output of DFT calculations. We begin by illustrating how phonon band structures can validate the DFT-CP approach. For some intermetallic crystal structures, such as the Laves phases, the details of the packing geometries make the resulting CP scheme very sensitive to assumptions about how space should be partitioned among the interatomic contacts. Using the Laves phase CaPd2 (MgCu2 type) as a model system, we demonstrate how the phonon band structure provides a reference against which the space-partitioning method can be refined. A key parameter we identify is the ionicity of the crystal structure: the assumption of some electron transfer from the Ca to the Pd leads to a close agreement between the CP distribution and the major features of its phonon band structure. In particular, atomic motions along directions of positive CP (indicative of overly short interatomic distances) contribute to high frequency modes, while those along negative CPs (corresponding to overly long distances) make up the lowest frequency modes. Finally, we apply this approach to Nb3Ge (Cr3Si type) and CaPd5 (CaCu5 type), for which low-frequency. phonon modes correlate with superconductivity and a rich variety of superstructures, respectively. Through these examples, CP analysis will emerge as a means of predicting the presence of soft phonon modes in a crystal structure and a guide to how elemental substitutions will affect the frequencies of these modes.