Origin of NMR shielding in fluorides
In this work, we analyze in detail the relation between electronic structure and fluorine nuclear magnetic resonance (NMR) shielding in a series of solid state alkali fluorides (LiF, NaF, KF, RbF, and CsF). For that purpose, we use solid-state NMR calculations implemented in the density functional theory full potential WIEN2K code (APW + lo). Both measurements and calculations show that the NMR shielding varies across the series by approximately 200 ppm. We focus our discussion on an explanation of the origin of the observed trend, and we show that the variation is mainly determined by contributions from “semicore” metal-p and valence F-p bands. More specifically, the trend in fluorine shielding can be related to the small but significant change in the hybridization of these states. A second important ingredient determining the value of the shielding is the presence and position of metal-d states in the unoccupied part of the Kohn-Sham bands. Although the present analysis has been demonstrated for the 19F nucleus in alkali fluorides, the main results are more general and can explain similar trends observed in other solids and for other nuclei.
Computational Study of Al and Sc NMR Shielding in Metallic ScTT′Al Heusler Phases
The results of first-principles calculations of Al and Sc NMR shielding for a set of ScTT′Al Heusler phase compounds are reported and compared to recently published experimental NMR shifts. The orbital component of the shielding (chemical shift) is computed using density functional perturbation formalism. The spin part (Knight shift) is evaluated using a direct self-consistent approach, where a finite external magnetic field acting on the electron spin is added to the density functional theory (DFT) Hamiltonian. Both approaches are implemented in the full potential linearized augmented plane wave method. We show that, for Al, the calculated and measured shifts match quite well except for the ScNiAuAl case, which is probably due to an experimental problem as the reported lattice parameter is also unrealistic. For Sc nuclei, we find three such unmatched cases between theory and experiment and we discuss possible sources of this discrepancy. For selected compounds, the effects of composition and lattice size...
On the use of the Hardening Soil Small Strain model in geotechnical practice
This article highlights the importance of using advanced constitutive soil models in numerical modelling as daily geotechnical practice. In this context, the Hardening Soil (HS) model is presented as the most advanced soil model implemented in the ZSoil finite element code. The article recalls the basic features of the HS model and it explains their role in numerical simulations. The role of pre-failure non-linear behaviour of soils is also discussed. An application of the HS model is illustrated on typical geotechnical problems such as retaining wall excavation, tunnel excavation and undrained loading followed by consolidation.