Solid State Communications 150 (2010) 1262–1267 Contents lists available at ScienceDirect Solid State Communications journal homepage: www.elsevier.com/locate/ssc Magnetic susceptibility and Knight shift of PdH x M. Deng, H. Freyer, S. Mankovsky, H. Ebert ∗ , J. Voitländer Department of Chemistry, University of Munich, Butenandtstrasse 11, D-81377 Munich, Germany article info Article history: Received 9 March 2010 Accepted 21 March 2010 by H. Akai Available online 23 April 2010 Keywords: A. H-transition metal systems A. H-storage materials D. Magnetic susceptibility D. Knight shift abstract The electronic properties of the system PdH x have been calculated by means of the self-consistent relativistic KKR-CPA (Korringa–Kohn–Rostoker Coherent Potential Approximation) method of band structure calculations for disordered systems. Using a linear response formalism, the magnetic susceptibility and Knight shift of PdH x have been investigated thoroughly. The corresponding results are discussed in detail in comparison with experimental data. In particular, it is shown that for low H concentrations the H Knight shift is determined by a transferred negative contribution due to the high partial spin susceptibility of Pd. © 2010 Elsevier Ltd. All rights reserved. 1. Introduction More than a hundred years ago, it was already observed that Pd absorbs large amounts of H to form PdH x [1]. Since then the PdH x system became the most intensively studied metal/gas system, often with the focus of the use of PdH x as an efficient H storage system [2–4]. Older studies on PdH x found that this system does not behave like a stoichiometric compound but like a homogeneous alloy in which the dissolved H plays the role of an alloy partner. The dissolution of H in the Pd lattice and the formation of a metal hydride perturb the electronic and phononic structures of the host metal considerably. Accordingly, studying the electronic properties of this system is not only of fundamental interest for understanding the H–metal interaction but also sheds light on its important properties, such as the heat of formation, heat conductivity, H embrittlement, catalysis, superconductivity, electric resistivity and magnetic properties [5]. Concerning theoretical studies up to the early 1970s, oversimplified models were often used for describing the bond- ing mechanism of H in transition metals [6]. The first ab ini- tio band-structure calculations on binary hydrides performed by Switendick [7] gave a new impetus and stimulated a lot of exper- imental and theoretical work. Later band-structure studies were restricted at the beginning to stoichiometric compounds [7–10]. This restriction could be removed by making use of the CPA (Co- herent Potential Approximation) alloy theory in connection with the tight-binding method [8,11] as well as the more reliable KKR (Korringa–Kohn–Rostoker) [12,13] band-structure method. These ∗ Corresponding author. Tel.: +49 (0) 89 2180 77583; fax: +49 (0) 89 2180 77584. E-mail address: hubert.ebert@cup.uni-muenchen.de (H. Ebert). ab initio calculations, in which the role of the chemical bonding has been emphasised, demonstrated that the conventional crude rigid-band model in either its protonic or anionic form is not safely applicable for interpreting the electronic structure and the exper- imental data of PdH x . The magnetic susceptibility of PdH x has often been used to follow the changes of the electronic structure as a function of the H content x [14–17]. In contrast to the magnetic susceptibility, the Knight shift of Pd and H in PdH x allows one to study element-specific electronic properties. Within the present work, the relativistic version of the KKR-CPA has been used to investigate the electronic properties of PdH x . Making use of linear response formalism, the magnetic susceptibilities and Knight shifts in PdH x were calculated and used for a detailed discussion of the available experimental data. 2. Theoretical framework The non-stoichiometric PdH x system is described by two interpenetrating fcc sublattices, one of which is the ordered Pd sublattice and the other a substitutionally disordered H-vacancy system. The corresponding electronic structure calculations were performed self-consistently by means of the relativistic KKR-CPA using the parameterisation for the exchange-correlation potential due to Vosko et al. [18]. For the lattice parameter of PdH x , an estimate was used based on the value for pure Pd (7.322 Å) and the change in the relative volume v/v found by experiment and given by (0.19 ± 0.01) × x [5]. The calculations of the response function spin and orbital magnetic susceptibility and Knight shift were performed by an extension of the scheme introduced before for the treatment of 0038-1098/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2010.04.001