A Tour of Soft Atomic Motions: Chemical Pressure Quadrupoles Across Transition Metal–Main Group 1:2 Structure Types

Abstract

The rational design of materials requires an understanding of the relationships between structure and properties. In some fields, advances in computational tools and modeling have mapped out many of these connections. In the realm of intermetallics, however, principles for such relationships are still needed. Recently, we illustrated how the DFT–Chemical Pressure (CP) analysis can link geometrical motifs within crystalline arrangements to the phonon band structures of intermetallics and thus the physical properties related to vibrations and atomic motion. The key indicators here are quadrupolar CP featuresdistributions in which positive and negative interatomic pressures are oriented perpendicular to one another. These quadrupoles then create low energy paths of motion for the atoms that can be linked to various structural phenomena, such as anisotropic vibrations and incommensurate modulations. In this article, we survey the presence of CP quadrupoles in a collection of TE2 structures (T = transition metal and E = main group element) and the roles they play in the behavior observed for these compounds. We begin by developing a metric for CP quadrupolar character, which can be calculated from the output of CP analysis. After compiling these metrics for 17 TE2 structure types, we delve deeper into four systems detected as exhibiting atomic sites with quadrupolar character: (1) the Co–Sn binary system, where the quadrupoles on the Co atoms in CuAl2-type CoSn2 direct the features of its superstructure in CoSn3; (2) arsenopyrite-type CoSb2, in which the highly quadrupolar CP distributions on the Sb atoms correlate with the motions followed during the phase transition to its high-temperature marcasite-type form; (3) the CrSi2 structure, in which the expansion of the lattice is predicted to open a helical path of potential soft motion analogous to that underlying the Nowotny Chimney Ladder series; and (4) the CdAs2 type, whose CP features anticipate the ability to incorporate Li atoms as guests. Together, these case studies highlight the potential for CP quadrupoles to link local atomic arrangements with a variety of emergent properties in intermetallic phases.

Emergent Transitions: Discord between Electronic and Chemical Pressure Effects in the REAl3 (RE = Sc, Y, Lanthanides) Series

“…This can be judged from the quadrupolar character of the CP features of the atomic sites, high values of which are connected to modes of soft atomic motion . The quadrupolar character, as measured by the recently developed QP metric, is significantly higher for Al atoms in the AuCu 3 type than in Ni 3 Sn type (see Table ), consistent with the d orbital-like shape of the Al CP features in the former. This suggests that higher temperatures would tend to enhance the AuCu 3 -type features of a structure.…”

The Intermetallic Reactivity Database: Compiling Chemical Pressure and Electronic Metrics toward Materials Design and Discovery

“…This creates a strong quadrupolar character. 60 When we exchange Pd with larger Ag atoms, the Ca atom becomes smaller relative to its environment; this is detectable in the vanishing of the positive CP features in the ab plane around the Ca atom, with the Ca CP surface now appearing with an hour-glass pattern defined by large negative lobes that touch at the atomic center. In CaCd 5 , with the Cd atoms being larger than the Ag or Pd ones, this trend continues with negative CP arising in the ab plane around the Ca atom.…”

“…While the Pd neighbors in the planes above and below along c are too distant, those in the same plane are too close. This creates a strong quadrupolar character . When we exchange Pd with larger Ag atoms, the Ca atom becomes smaller relative to its environment; this is detectable in the vanishing of the positive CP features in the ab plane around the Ca atom, with the Ca CP surface now appearing with an hour-glass pattern defined by large negative lobes that touch at the atomic center.…”

Entropic Control of Bonding, Guided by Chemical Pressure: Phase Transitions and 18-n+m Isomerism of IrIn3

“…The quadrupolar character of an atom can be quantified with the quadrupole metric (QP): where the c l , m coefficients refer to the contributions of the Y l , m spherical harmonics to the angular CP distribution around the atom: …”

“…One of the most significant motifs to arise in CP schemes, the quadrupole, features positive and negative pressures oriented perpendicularly to each other, creating dorbital-like distributions. 51 Such motifs are familiar from our analysis of the CoGa 3 type. The CP lobes on the E atoms capping the T-centered trigonal prisms define a d z2 -shaped arrangement (Figures 5a and 6a,b), with positive pressures pointing towards T atoms and a perpendicular ring of negative pressures pointing into the void spaces.…”