Pd_0.213Cd_0.787 and Pd_0.235Cd_0.765 Structures: Their Long c Axis and Composite Crystals, Chemical Twinning, and Atomic Site Preferences

Abstract

We present single-crystal studies of Pd(0.213)Cd(0.787) and Pd(0.235)Cd(0.765), synchrotron powder studies of Pd(1-x)Cd(x), 0.755> or =x> or =0.800, and LDA-DFT and extended Hückel (eH) calculations on these or related phases. The two single-crystal structures have a, b, and c axis lengths of 9.9013(7), 14.0033(10), 37.063(24) and 9.9251(3), 14.0212(7), 60.181(3) A, respectively and they crystallize in the space groups Ccme and F2mm, respectively (solved as (3+1)-dimensional crystals their most convenient superspace group is Xmmm(00gamma)s00). The structures have two different structural components each with their own separate axis parameters. Powder data shows that the ratio of these separate axes (S/L) varies from 1.615 to 1.64, values near the golden mean (1.618). For Pd(0.213)Cd(0.787), different Pd and Cd site occupancies lead to variation in the R factor from 2.6-3.6 %. The site occupancy pattern with the lowest R factor (among the 26 820 variants studied) is the exact site occupancy pattern predicted by LDA-DFT parameterized eH Mulliken charge populations. The phases can be understood through a chemical twinning principle found in gamma-brass, the parent structure for the above phases (a relation with the MgCu(2) Laves phase is also noted). This twinning principle can be used to account for Cd and Pd site preferences. At the same time there is a clean separation among the Cd and Pd atoms for the two separate chain types at height b=0 and 1/2. These results indicate that Cd:Pd stoichiometry plays a role in phase stability.

Mg11Cu6Al12, A New Link in the Structural Chemistry of MgCu2‐Type Clusters

“…Later, this approach was applied to intermetallic phases, providing insights into and predictions of site-preferences, [28,29] and guidance for those navigating the multitude of possible descriptions of complex crystal structures. [10,30,31] Let's start with a review of what this type of analysis tells us about the Mg 17 Al 12 structure, [10] for contrast with the results we will find for Mg 11 (2 ϫ 17 + 3 ϫ 12)/(17 + 12) = 2.41 electrons/atom. This is envisioned as representing a version of this phase without Al/Mg ordering, but in practice is achieved by beginning with Al eH parameters and tuning them to achieve a qualitative match with a band structure calculated with DFT.…”

Synthesis of a Large Functional Cage Compound Based on Four GaGa Single Bonds and Its Application as an Oligoacceptor: On the Way to Bio‐Organogallium Hybrid Molecules

“…In γ‐brass itself (Cu 5 Zn 8 ), for example, Zn atoms occupy the IT and CO sites shown in gray, while Cu atoms occupy OT and OH shown in green 23. More generally, electronic structure calculations have shown that the less electronegative element in a γ‐brass variant prefers the IT and CO sites, while the more electronegative element prefers OT and OH 24…”

“…Using the same “generic” atomic parameters at all atomic sites in Mg 44 Rh 7 , Mulliken populations were calculated, and the more electronegative Rh atoms were assumed to prefer sites with larger Mulliken populations. This assumption has been successfully employed to derive intermetallic site preferences many times in the past 24. 32–36 Before Mulliken populations could be calculated, atomic parameters for the eH calculation of Mg 44 Rh 7 were calibrated against LDA‐DFT calculations to ensure that they were physically reasonable.…”

“…While not identical to the LDA‐DFT band structure, the calibrated eH band structure mimics many of the LDA‐DFT features, especially near the Fermi energy. Such calibration methods have proven reliable in the past 24. 36, 46–48…”

Sich durchdringende polare und unpolare Untergitter in intermetallischen Phasen: die Struktur von NaCd2

“…Rechnungen mit dem YAeHMOP-Programmpaket wurden mit voreingestellten Cd-Parametern durchgeführt: [95] H ii (5s) = À11.8 eV, H ii (5p) = À8.2 eV, z(5s) = 1.64, z(5p) = 1.60. Die LDA-DFT-Bandstruktur der kubischen g-MessingStruktur [96] wurde mit diesen Cd-Parametern gut reproduziert. ¾hnlich wie NaCd 2 …”