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Whilst it has long been known that disorder profoundly affects transport properties, recent measurements on a series of solid solution 3d-transition metal alloys reveal two orders of magnitude variations in the residual resistivity. Using ab-initio methods, we demonstrate that, while the carrier density of all alloys is as high as in normal metals, the electron mean-free-path can vary from ~10 Å (strong scattering limit) to ~10 3 Å (weak scattering limit). Here, we delineate the underlying electron scattering mechanisms responsible for this disparate behavior. While site-diagonal, spin dependent, potential scattering is always dominant, for alloys containing only Fe, Co, and Ni the majority spin channel experiences negligible disorder scattering, thereby providing a short circuit, while for Cr/Mn containing alloys both spin channels experience strong disorder scattering due to an electron filling effect. Somewhat surprisingly, other scattering mechanisms -including displacement, or size effect, scattering which has been shown to strongly correlate with such diverse properties as yield strength -are found to be relatively weak in most cases 4 component equiatomic fcc solid solutions: NiPd, NiCo, NiFe, NiFeCo, NiCoCr, NiCoMn, NiCrCoMn, NiFeCoMn and NiFeCoCr. This set of alloys combined with NiFeCoCrMn and NiFeCoCrPd (here collectively referred to as Cantor-Wu alloys), constitute a rich playground for comprehensive studies of the role of maximal disorder on the properties of multi-component alloys by controlling both the number (increasing configurational entropy) and types (chemical specificity) of alloying elements 4,5,8 . Of interest here are the results of recent residual resistivity measurements 5,8 of a subset of Cantor-Wu alloys that show, rather than increasing monotonically with increasing numbers of components, values of r0 break into two subgroups of low (r0 <10 µW•cm) and high (r0 >75 µW•cm) resistivity alloys. In addition, two entropically identical alloys, NiCoFe (r0 = 1.7µW•cm) and NiCoCr (r0 =92.7 µW•cm), fall into different resistivity groupings. Remarkably, the least and most resistive alloys differ by almost two orders of magnitude, r0(NiCo)=1.3µW•cm; r0(NiFeCoCrPd)=124.8µW•cm. Interestingly, the low resistivity group have r0 values typical of dilute weak scattering alloys in which there are clearly defined host (solvent) and impurity (solute) elements. In such alloys, r0 arises from the scattering of a low Fermi energy DOS of nearly-freeelectron sp-states with large λ e [ε F ] and r0 generally obeys both Nordheim's relation (r0∝c((1-c);where c is impurity concentration) 9 and Linde's "law" (r0 ∝ (DZ) 2 ; where DZ is the valence difference between host and impurity atoms) 10 . (see Ref. 11 for a discussion) This, despite the fact that, in equiatomic alloys, the concept of host and impurity elements is lost and the Fermi energy falls in the high density of state (DOS) d-bands 5 . At the other extreme, high-r0 NiFeCoCrPd is

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New convenient wet-chemistry synthetic routes have made it possible to explore catalytic activities of a variety of single supported atoms, however, the single supported atoms on inert substrates (e.g. alumina) are limited to adatoms and cations of Pt, Pd, and Ru. Previously, we have found that single supported Pt atoms are remarkable NO oxidation catalysts. In contrast, we report that Pd single atoms are completely inactive for NO oxidation. The diffuse reflectance infra-red spectroscopy (DRIFTS) results show the absence of nitrate formation on catalyst. To explain these results, we explored modified Langmuir-Hinshelwood type pathways that have been proposed for oxidation reactions on single supported atom. In the first pathway, we find that there is energy barrier for the release of NO2 which prevent NO oxidation. In the second pathway, our results show that there is no driving force for the formation of O=N-O-O intermediate or nitrate on single supported Pd atoms. The decomposition of nitrate, if formed, is an endothermic event.

Carlomethods or the CVM. The difficulty with such an approacnistnatcomplex electronically mediatedinteractions aremapped ontoaneffective classical Hamiltonian. Unfortunately, thereisno apriori guarantee thatsucha procedure iseither uniqueor " rapidly convergent. In addition, since theparameters areextracted from calculations on smallunitcell systems, thereispossible thattheinteractions contain contributions (e.g. fromtheMadelnng energy) thatwill excessively favor suchstructures withrespect tothe disordered phase. Inthese lecture noteswe shall reviewtheLDA-KKR-CPA method fortreating the electronic structure and energetics ofrandom alloys and theMF-CF and GPM theories ofordering and phasestability thathavebeenbuilt on theLDA-KKR-CPA description ofthedisordered phase.Thus,we takethepoint ofviewthatmuch can be learned about metallic alloys by first studying theelectronic structure and energetics ofideal random solid solutions, which,forentropic reasons, arethenatural hightemperature solid state phasesand thento investigate their instabilities to theeither phaseseparation or to theformation ofspecific orderedphases. We shall stress thata direct connection can oftenbe made betweenspecific features intheelectronic structure associated withthe random solid solution and thedriving mechanismsbehindspecific ordering phenomena. Consequently, our understanding ofphasestability willbe underpinned by the same electronic structure thatisresponsible fordetermining theresidual resistivity and other properties ofthedisordered phaseand thatcan be experimentally verified usingoptical spectroscopies, positron annihilation and otherprobes. These lecture notesare structured as follows. In section 2 we layout the basic LDA-KKR-CPA theory oftheelectronic structure and energetics ofrandom alloys and some examplesof itsapplications to theelectronic structure and energie_ ofrandom alloys arepresented. In section 3 we reviewtheprogress thathas beenmade overthe last few yearsin understanding the mechanismsbehindspecific ordering phenomena observed inbinarysolid solutions basedon theMF-CF and GPM theories ofordering and phasestability. We will giveexamplesofa variety ofordering mechanisms:Fermi surface nesting, band filling, off diagonal randomness, charge transfer, size difference or local strain fluctuations, and magnetic effects. Ineachcasewe will trytomake thelink betweenthespecific ordering phenomenon and the underlying electronic structure of thedisordered phase.Insection 4 we will review theresults ofsome recent calculations on theelectronic structure of_-phaseNicAl1_c alloys usinga version oftheLDA-KKR-CPA codes that has been generalized to systems having complex lattices. In section 5 " we provide a few concluding remarks. 2 Theory of Random Substitutional Alloys 2.1 LDA-KKR-CPA The LDA-KKR-CPA method for calculating the energy and other properties of random solid solution alloys rests on three theoretical developments: the local density approximation to density functional theory, multiple scattering theory for solving the effective si...