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While composition and pressure are generally considered orthogonal parameters in the synthesis and optimization of solid state materials, their distinctness is blurred by the concept of chemical pressure (CP): microscopic pressure arising from lattice constraints rather than an externally applied force. In this article, we describe the first cycle of an iterative theoretical/experimental investigation into this connection. We begin by theoretically probing the ability of physical pressure to promote structural transitions in CaCu5-type phases that are driven by CP in other systems. Our results point to the instability of the reported CaCu5-type CaPd5phase to such a transition even at ambient pressure, suggesting that new structural chemistry should arise at only modest pressures. We thus attempted to synthesize CaPd5as a starting material for high-pressure experiments. However, rather than obtaining the expected CaCu5-type phase, we encountered crystals of an incommensurately modulated variant CaPd5+q/2, whose composition is related to its satellite spacing, q= qbbasic* with q≈ 0.44. Its structure was solved and refined in the (3 + 1)D superspace group Cmcm(0β0)s00, revealing CaCu5-type slabs separated by distorted Pd hexagonal nets with an incommensurate periodicity. DFT-CP analysis on a commensurate model for CaPd5+q/2indicates that the new Pd nets serve to relieve intense negative CPs that the Ca atoms would experience in a CaCu5-type CaPd5phase but suffer from a desire to contract relative to the rest of the structure. In this way, both the Pd layer substitution and incommensurability in CaPd5+q/2are anticipated by the CP schemes of simpler model systems, with CP quadrupoles tracing the paths of the favorable atomic motions. This picture offers predictions for how elemental substitution and physical pressure should affect these structural motifs, which could be applicable to the magnetic phase Zr2Co11whose previously proposed structures show close parallels to CaPd5+q/2.

The notion of atomic size poses an important challenge to chemical theory: empirical evidence has long established that atoms have spatial requirements, which are summarized in tables of covalent, ionic, metallic, and van der Waals radii. Considerations based on these radii play a central role in the design and interpretation of experiments, but few methods are available to directly support arguments based on atomic size using electronic structure methods. Recently, we described an approach to elucidating atomic size effects using theoretical calculations: the DFT-Chemical Pressure analysis, which visualizes the local pressures arising in crystal structures from the interactions of atomic size and electronic effects. Using this approach, a variety of structural phenomena in intermetallic phases have already been understood in terms that provide guidance to new synthetic experiments. However, the applicability of the DFT-CP method to the broad range of the structures encountered in the solid state is limited by two issues: (1) the difficulty of interpreting the intense pressure features that appear in atomic core regions and (2) the need to divide space among pairs of interacting atoms in a meaningful way. In this article, we describe general solutions to these issues. In addressing the first issue, we explore the CP analysis of a test case in which no core pressures would be expected to arise: isolated atoms in large boxes. Our calculations reveal that intense core pressures do indeed arise in these virtually pressure-less model systems and allow us to trace the issue to the shifts in the voxel positions relative to atomic centers upon expanding and contracting the unit cell. A compensatory grid unwarping procedure is introduced to remedy this artifact. The second issue revolves around the difficulty of interpreting the pressure map in terms of interatomic interactions in a way that respects the size differences of the atoms and avoids artificial geometrical constraints. In approaching this challenge, we have developed a scheme for allocating the grid pressures to contacts inspired by the Hirshfeld charge analysis. Here, each voxel is allocated to the contact between the two atoms whose free atom electron densities show the largest values at that position. In this way, the differing sizes of atoms are naturally included in the division of space without resorting to empirical radii. The use of the improved DFT-CP method is illustrated through analyses of the applicability of radius ratio arguments to Laves phase structures and the structural preferences of AB5intermetallics between the CaCu5and AuBe5structure types.