Tutorial on Chemical Pressure Analysis: How Atomic Packing Drives Laves/Zintl Intergrowth in K3Au5Tl

Interface Nuclei in the Y-Ag-Zn System: Three Chemical Pressure-Templated Phases with Lamellar Mg2Zn11- and CaPd5+x-Type Domains

The interface nucleus approach was recently presented as a framework for understanding and predicting the emergence of modular intermetallic phases, i.e., complex structures derived from the assembly of units from simpler parent structures. Here, we present the synthesis and crystal structures of three new modular intermetallics in the Y-Ag-Zn system that support this strategy: YAg2.79Zn2.80 (I), YAg2.44Zn3.17 (II), and YAg2.71Zn2.71 (III). Each of these structures is derived from an intergrowth of slabs of the Mg2Zn11 and CaPd5+x types, with the chief differences being in the thickness and degree of disorder within the CaPd5+x-type domains. The merging of the parent structure domains is facilitated by their sharing a common geometrical unit, a double hexagonal antiprism. The use of this motif as an interface nucleus mirrors its role in another family of structures: an intergrowth series combining the CaCu5 and Laves phase structure types, as in the PuNi3-type phase YNi3. However, there is a key difference between the two series. While in the CaCu5/Laves intergrowths, the interface between the parent structures arises perpendicular to the interface nucleus's unique (hexagonal) axis, in the Mg2Zn11/CaPd5+x-type intergrowths revealed here, the interfaces run parallel to this axis. Using CP analysis of the Mg2Zn11/CaPd5+x-type parent structures, we trace this behavior to the different directions of high-CP compatibility of the interface nuclei in the Mg2Zn11/CaPd5+x and CaCu5/Laves structure type pairs. In this way, the Y(Ag/Zn)5+x phases highlight the role that interface nuclei play in directing the domain morphologies of modular intermetallic phases.

Toward Predicting the Assembly of Modular Intermetallics from Chemical Pressure Analysis: The Interface Nucleus Approach

Complex intermetallic phases are often constructed from domains derived from simpler structures arranged into hierarchical assemblies. These modular arrangements offer intriguing prospects, such as the integration of the properties of distinct compounds into a single material or for the emergence of new properties from the interactions among different domains. In this article, we develop a strategy for the design of such complex structures, which we term the interface nucleus approach. Within this framework, the assembly of complex structures is facilitated by interface nuclei: geometrical motifs shared by two parent structures that serve as a region of overlap to nucleate or seed the formation of a combined structure. Our central hypothesis is that the formation of an interface between structures at these motifs creates opportunities for the relief of atomic packing stresses, as revealed by Density Functional Theory-Chemical Pressure (DFT-CP) analysis: when corresponding interatomic contacts in two structures exhibit complementarity─negative CP with positive CP or intense CP with mild CP─the intergrowth allows for a more balanced packing arrangement. To illustrate the application of the interface nucleus concept, we analyze three modular intermetallic structures, the σ-phase (FeCr), PuNi3, and Ca6Cu6Al5 types. In each case, the assembly of the structure can be connected to complementary CP features in an interface nucleus shared by its parent structures, while the distribution of the interface nuclei in the parents serves to template the geometry of the overall framework. In this way, the interface nucleus approach points toward avenues for the design of modular intermetallics from the CP schemes of potential partner structures.

As predicted and more: modulated channel occupation in YZn5+x

Like many complex intermetallic phases, the crystal structures of REZn5+x compounds (RE = lanthanide or Group 3 element) based on the EuMg5 type have gradually unfolded. The original reports described a complex hexagonal structure with an unusual combination of tetrahedrally close-packed regions and open spaces, as well as observations of superstructure reflections. More recently, we reinvestigated the structure of YZn5, reclassifying it as the EuMg5+x-type compound YZn5+x (x ≃ 0.2), in which disordered channels run along c through the spaces formerly considered open. In addition, DFT-chemical pressure (DFT-CP) analysis of ordered models of YZn5+x highlighted paths for communication between neighboring channels setting the stage for superstructure formation. Herein, the experimental elucidation of this effect is presented with the synthesis and structure determination of a modulated form of YZn5+x. By slow-cooling samples of YZn5+x from the annealing temperature, crystals were obtained that exhibit satellite reflections with the modulation wavevector q = {1\over 3}a* + {1\over 3}b* + 0.3041c*. Structure solution and refinement using a (3+1)D model in superspace group P31c({1\over 3}\,\!{1\over 3}σ3)00s reveals incommensurate order in the structure's channels. Here, two Zn sites associated with the channels are present, each with discontinuous atomic domains that are slanted in the x3x4 plane. Their slanting corresponds to adjustments along the c axis for the presence or absence of close neighbors along that axis, while the occupation patterns of neighboring channels are shifted by {1\over 3} of the modulation period. These features follow earlier predictions from CP analysis, highlighting how this approach can be used predictively in search of new phenomena.

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

Atomic packing and electronic structure are key factors underlying the crystal structures adopted by solid-state compounds. In cases where these factors conflict, structural complexity often arises. Such is born in the series of REAl₃ (RE = Sc, Y, lanthanides), which adopt structures with varied stacking patterns of face-centered cubic close packed (FCC, AuCu₃ type) and hexagonal close packed (HCP, Ni₃Sn type) layers. The percentage of the hexagonal stacking in the structures is correlated with the size of the rare earth atom, but the mechanism by which changes in atomic size drive these large-scale shifts is unclear. In this Article, we reveal this mechanism through DFT-Chemical Pressure (CP) and reversed approximation Molecular Orbital (raMO) analyses. CP analysis illustrates that the Ni₃Sn structure type is preferable from the viewpoint of atomic packing as it offers relief to packing issues in the AuCu₃ type by consolidating Al octahedra into columns, which shortens Al-Al contacts while simultaneously expanding the RE atom's coordination environment. On the other hand, the AuCu₃ type offers more electronic stability with an 18-n closed-shell configuration that is not available in the Ni₃Sn type (due to electron transfer from the RE d_z² atomic orbitals into Al-based states). Based on these results, we then turn to a schematic analysis of how the energetic contributions from atomic packing and the electronic structure vary as a function of the ratio of FCC and HCP stacking configurations within the structure and the RE atomic radius. The minima on the atomic packing and electronic surfaces are non-overlapping, creating frustration. However, when their contributions are added, new minima can emerge from their combination for specific RE radii representing intergrowth structures in the REAl₃ series. Based on this picture, we propose the concept of emergent transitions, within the framework of the Frustrated and Allowed Structural Transitions principle, for tracing the connection between competing energetic factors and complexity in intermetallic structures.

Chemical pressure in functional materials

Chemical pressure, a strange but familiar concept, is a lattice internal force caused by lattice strain with chemical modifications and arouses great interest due to its diversity and efficiency to synthesize new compounds and tune functional materials. Different from physical pressure loaded by an external force that is positive, chemical pressure can be either positive or negative (contract a lattice or expand it), often through flexible and mild chemical synthesis strategies, which are particularly important as a degree of freedom to manipulate material behaviors. In this tutorial review, we summarize the features of chemical pressure as a methodology and demonstrate its role in synthesizing and discovering some typical magnetically, electrically, and thermally responsive functional materials. The measure of chemical pressure using experimental lattice strain and elastic modulus was proposed, which can be used for quantitative descriptions of the correlation between lattice distortion and properties. From a lattice strain point of view, we classify chemical pressure into different categories: (i) chemical substitution, (ii) chemical intercalation/de-intercalation, (iii) size effect, and (iv) interface constraint, etc. Chemical pressure affects chemical bonding and rationalizes the crystal structure by modifying the electronic structure of solids, regulating the lattice symmetry, local structure, phonon structure effects etc., emerging as a general and effective method for synthesizing new compounds and tuning functional materials.

Buffering Octahedra in Mo4Zr9P: Intergrowth as a Solution to the Frustrated Packing of Tricapped Trigonal Prisms and Icosahedra

Atomic packings based on icosahedra and tricapped trigonal prisms are prone to frustration─indeed, these polyhedra represent common configurations in metallic glasses. In this Article, we illustrate how these packing issues can serve as a driving force for the formation of modular intermetallic structures. Using Density Functional Theory-Chemical Pressure (DFT-CP) analysis, we relate the Hf₉Mo₄B-type structure of Mo₄Zr₉P to interatomic pressures experienced by the atoms in two parent structures: Zr₃P, whose structure is built from tricapped trigonal prisms, and ZrMo₂, a Laves phase containing icosahedra. CP analysis of Zr₃P reveals that it has particularly frustrated packing because of the entangling of its tricapped trigonal prisms. In the ternary phase, the frustration is significantly relieved as the units become isolated from each other. Further analysis points to the stabilizing effect of a face-sharing network of octahedra in Mo₄Zr₉P that largely separates the structure into Zr-Mo and Zr-P domains and serves as a buffering region for the relaxation of interatomic distances. These conclusions are generalized to the broader members of this structure type with the examination of the CP schemes for the isostructural Mo₄Zr₉B, Al₅Co₂, and Mg₅Pd₂ phases. Finally, we screen the structural literature using the ToposPro software to identify three additional structure types that have similar intergrowth patterns: the Dy₄CoCd, La₂₃Ni₇Mg₄, and Gd₁₄Co₃In₃ types. An analysis of the interatomic distances within the octahedral networks of these structures suggests that these networks commonly facilitate the reconciliation of packing incompatibilities in intermetallic chemistry.