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.