David G. Pettifor

Perspectives of giant magnetoresistance

Publisher Summary This chapter discusses the physics of giant magneto resistance (GMR). The chapter emphasizes the role of the spin-polarized electronic band structure that is crucial for understanding GMR. The origin of GMR and a simple resistor model has been introduced in the chapter. The experimental data on current-in-the-plane (CIP) GMR in magnetic multilayers, spin valves, dependence of GMR on composition, layer thickness, roughness, impurities, outer boundaries, and temperature have also been discussed in the chapter. The theoretical formulations of GMR within free electron and simple tight-binding models have been reviewed from the semiclassical and quantum mechanical viewpoints. Multiband models for GMR have also been reviewed. The semiclassical and quantum mechanical approaches to GMR within the diffusive limit and the interpretation of selected experimental results have been presented in the chapter.

Electronic structure, phase stability and elastic moduli of AB transition metal aluminides

Abstract Binding energy curves for the 4d transition metal TM aluminides TMAl with respect to 12 different AB-structure types have been computed using the full-potential linear muffin-tin orbitals (FP-LMTO) method within local-density-functional approximation (LDA). Combining with our previous calculations for the 3d TMAl, we find that the observed ground state structures are predicted correctly for all the AB transition metal aluminides including the low-temperature monoclinic C2/m phase of CuAl. Moreover, the B32 phase is predicted to be the most stable amongst competing metastable phases for CrAl, MoAl, TcAl, whereas for VAl and NbAl the most stable phases are L10 and Ω , respectively. The calculated heats of formation are in good agreement with available experimental data. The critical roles played by the average number of valence electrons per atom and the angular character of the valence orbitals are emphasized in explaining the structural phase stability across the TMAl series. In particular, it is shown that the structural trend going from B2 (bcc-like) → L10 (fcc-like) → B19 (hcp-like) → B2 as a function of electron concentration, can be understood from a band structure energy analysis. The calculated electronic structure for all the stable phases of both the 3d and 4d TMAl demonstrates a correlation between structural stability and the shape of the density of states due to the strong directional bonding between the sp(Al) and d(TM) orbitals. Finally, the elastic moduli have been computed for all observed ground states of TMAl with new results for ScAl and RhAl (in the B2 structure), YAl and ZrAl (in the B33 structure) and for PdAl (in the B20 structure).

Atomistic simulation of titanium. II. Structure of ⅓ 〈1210〉 screw dislocations and slip systems in titanium

Abstract The bond-order potential for hcp Ti, constructed in part I, and a central-force Finnis-Sinclair-type potential have been used to study atomistically the core structure of the ⅓ 〈1210〉 screw dislocation. The qualitative features of the core structures are similar in the two cases. The dislocation may either dissociate into Shockley partials on the basal plane or spread in a continuous manner into the prism plane. However, the spreading of the dislocation core into the prism plane is always energetically favoured over the splitting into the basal plane in the case of the bond-order potential whilst the opposite is found in the case of the centralforce Finnis-Sinclair-type potential. Hence, the results obtained using the bond-order potential explain the strong preference for the prism slip over the basal slip in Ti. The most important global parameter is the energy of the intrinsic stacking fault on the basal plane which is so high in the case of the bond-order potential that splitting into Shockley...

Controlled orientation of ellipsoidal fullerene C70 in carbon nanotubes

Density functional theory calculations predict two orientations for ellipsoidal C70 fullerenes inside single-walled carbon nanotubes (SWNTs) of different sizes: transverse orientation for C70 in (11,11) nanotubes (d=14.9 A) and longitudinal orientation for C70 in (10,10) nanotubes (d=13.6 A). SWNTs with these diameters have been prepared and filled with the C70 fullerenes, and characterized by Raman spectroscopy and high-resolution transmission electron microscopy, showing the orientations predicted by theory.

Structure and metastability of mesoscopic vacancy and interstitial loop defects in iron and tungsten

The most recent observations of dynamical time-dependent fluctuating behaviour of mesoscopic radiation defects in body-centred cubic metals (Arakawa et al 2006 Phys. Rev. Lett. 96 125506; 2007 Science 318 956–9; Yao et al 2008 Phil. Mag. at press) have highlighted the need to develop adequate quantitative models for the structural stability of defects in the mesoscopic limit where defects are accessible to direct in situ electron microscope imaging. In pursuit of this objective, we investigate and compare several types of mesoscopic vacancy and interstitial defects in iron and tungsten by simulating them using recently developed many-body interatomic potentials. We show that the mesoscopic vacancy dislocation loops observed in ion-irradiated materials are, without exception, metastable with respect to the transformation into spherical voids, but that the rate of this transformation and even the specific type of the transformation mechanism depend on the defect size and the properties of the material.

A bandstructure view of the Hume-Rothery electron phases

The stability of Hume–Rotherys electron phases is studied using modern bandstructure techniques. For these alloys, empirical evidence has shown a strong correlation between the number of valence electrons per atom and the adopted crystal structure. The generally accepted explanation traces the phenomenon to prominent structure in the electron density of states which arises when the free–electron Fermi sphere encounters the Bragg planes at the surface of the Brillouin zone. By applying a rigid band model on the basis of density functional theory to the archetypal system Cu–Zn, we obtain accurate density–of–states functions which are used to critically evaluate the popular models due to Mott and Jones. We also are able to account for the stability of the γ–phase.

A comparison of linear scaling tight-binding methods

Four linear scaling tight-binding methods (the density matrix method, bond order potentials, the global density of states method, and the Fermi operator expansion) are described and compared to show relative computational efficiency for a given accuracy. Various example systems are explored: an insulator (carbon in the diamond structure), a semiconductor (silicon), a transition metal (titanium) and a molecule (benzene). The density matrix method proves to be most efficient for systems with narrow features in their energy gaps, while recursion-based moments methods prove to be most efficient for metallic systems.

Atomistic modelling of TiAl I. Bond-order potentials with environmental dependence

Bond-order potentials (BOPs) for L10 TiAl have been developed and constructed within a tight-binding framework. In addition to the usual attractive bond-energy contribution arising from the formation of covalent bonds and pairwise contribution describing the overlap repulsion and electrostatic interaction, we have included an environmentally dependent term to represent the strong repulsion experienced by the valence sp electrons in transition metals and their alloys. The latter contribution is crucial for reproducing the negative Cauchy pressures of TiAl and other transition-metal-based intermetallic compounds. The constructed BOPs have been tested in the following ways: firstly, examination of the mechanical stability of the tetragonal L10 lattice with respect to large deformations and other crystal structures with the same stoichiometry; secondly, calculation of the γ surface for {111} and related evaluation of the energies of stacking-fault-type defects; thirdly, calculation of energies of the γ-γ interfaces that are present in the lamellar TiAl and energies associated with the formations of point defects in TiAl. The results of all these calculations show very good agreement with various ab-initio calculations. Importantly, we find that this potential is transferable to the different bonding environment in the hexagonal D019 Ti3Al. Hence these BOPs are suitable for atomistic study of dislocations and other extended defects not only in L10 TiAl but also in Ti3Al and possibly structures with other titanium-rich stoichiometries.

Defect modelling: the need for angularly dependent potentials

Abstract The reliable atomistic simulation of defects in intermetallics requires the development of angularly dependent interatomic potentials. Ab initio calculations predict, for example, that the nearest competing phases to the L10 ground state of TiAl and the B2 ground state of NiAl are B33 (CrB) and B20 (FeSi) respectively, whose structural stability is determined by directional pd bonding. This is well described by the Tight Binding model, within which approximation angularly dependent many-atom interatomic potentials have recently been derived. The nature of these so-called Bond Order Potentials (BOPs) and their application to structural prediction in elemental d-valent transition metals and sp-valent semiconductors are discussed.

Metastability of the o-phase in transition-metal aluminides: First-principles structural predictions

Abstract A systematic total-energy study has been performed on the ω-phase of transition-metal-aluminide-based alloys using first-principles electronic structure calculations. The calculated o-phase heat of formation for ω-phase against the electron per atom ratio e/a is found to show the same trends as the measured diffuse ω peak for alloys with values of e/a between 3·3 and 4·7. Moreover, we predict that the ω-phase is the most stable amongst competing metastable phases for NbAl. ω collapse studies show a strong correlation between this transformation and a mechanical instability in the related B2 alloys at low temperatures. A partial ω-type shuffle is also predicted for Ni2Al alloys with e/a values close to 7 in the B82 structure type. As a result of these calculations, we are now able to study the phase diagrams of structurally important ternary alloys such as Ti[sbnd]Al[sbnd]V of Ti[sbnd]Al[sbnd]Nb.