Condensed matter consists of positively charged atomic nuclei and the electron glue which holds them together. Although it is attractive to attempt to oilodl it by nentral atoms interacting via. relatively weak pairwise ‘effective interactions’ in genbreak down the predictive and inter;retative power of the analysis. Hence, there is no substitute to forging a parameter-free and quantitative theory of the complex degenerate Fermi liquid ‘glue’ to complement phenomenological calculations. Such theory is the general aim of ’first-principles’ calculations of the electronic structure. This talk will concern past present and future first-principles calculations relevant it the state of compositional order in metallic alloys. Special attention will be paid to phaase insta bilities induced by Fermi Surface effects.

We present a study of the mixing energies and the effective cluster interactions which form the configurational part of the internal energy of Pd-Rh substitutional alloys. We discuss the tendency towards phase-separation and more generally phase stability. The effects of a substitutional ternary addition on the tendencies toward order or phase-separation are also reported. The Korringa-Kohn-Rostoker Coherent-Potential Approximation (KKR-CPA) is used to investigate the electronic structure effects and energetics of the random alloy. Moreover, we use the Generalized Perturbation Method (GPM), using the KKR-CPA random alloy as a reference medium, to investigate the effective interactions which determine phase stability. We briefly comment on other factors which may give important contributions to the total free-energy of the alloy. We also contrast the GPM with the Connolly-Williams approach for calculating phase diagrams from first-principles. Finally, we explore the inadequacies of the frozen-potential and Harris approximations to the energetics of alloying.

We have performed calculations of the electronic structure of the random substitutional bcc Fe1-xCrx alloys, using the spin-polarized, self-consistent Korringa, Kohn and Rostoker coherent potential approximation (KKR-CPA) method. This is a first principles method based on a local spin density approximation for electron exchange and correlation energy. For the iron-rich alloys, we find that the average moment decreases linearly with Cr concentration, although the individual moments show a different concentration dependence and the Cr moment is anti-parallel to the Fe moment. This system is similar to Fe1-xVx system, although some details are different.

Due to its technological importance, the Al-Ti system has received much attention lately. For example, TiAl3 (as well as TiAl) has a low density and very high elevatedtemperature strength. However, this compound forms in the tetragonal D022 structure which has low ductility. Recent studies [1,2] have tried to understand the role of tetragonal distortion and the effect of ternary additions [3] in stablizing the D022 relative to the L12.

Ground state structural energies and lattice constants of Al-Ti system have been studied using the linear muffin-tin orbital (LMTO) method. In particular, we examine the effects of various approximations for the potential on the structural energies of low-symmetry compounds such as Al3Ti. In order to stabilize Al3Ti, in the atomic sphere approximation, the Muffin-Tin correction is essential although the resulting c/a is 10% too large. The lattice constants calculated with the full-potential LMTO method are in complete agreement with experiments, indicating the importance of non-sphericity of the potential for low-symmetry systems.

We have used a full potential all electron LMTO total energy calculation with a true interstitial to establish a baseline understanding of pure γ-TiAl. The c and a lattice parameters, Bulk modulus and the Young's modulus are calculated and found to be in excellent agreement with reported experimental values.

The energetic factors leading to the stability of complex structures in Al-rich transition-metal compounds are analyzed via ab-initio band-theoretic total-energy calculations comparing the Al12W and Cu3Au structures. For nearly half-filled d-bands, the Al12W structure is preferred by 1 eV per transition-metal atom or more. The preference for complex structures results from effects related to the shape of the d-projected electronic density of states, which are found to be more important than atomic-size effects, and are directly related to the complexity of the structure.

Electronic structure and phase stability properties of Ni-Ti and Ni-Al around equiatomic composition are investigated with a first principles approach. The study is based upon the generalized purturbation method applied to the Korringa-Kohn-Rostoker multiple scattering formulation of the coherent potential approximation. Within this framework, effective cluster interactions which build up the configuration-dependent part of the internal energy are calculated. The strength of ordering tendencies in both bcc-based substitutional alloys is compared and contrasted in terms of hybridisation effects, in relation with experimental evidences.

The FCC superstructure phase diagram for Cu-Pd is calculated by means of isotropic effective interactions derived from an ab initio KKR-CPA electronic structure calculation. We prove the existence of a region in which one-dimensional long period superstructures are stable. This region is composed of several single phase fields in which the modulation period is constant. The value of the modulation period is in close agreement with results from High Resolution Electron Microscopy. Adding oxygen to Cu-Pd is found to sharpen the antiphase boundaries. This experiment enables us to clarify the role of the Fermi surface in these alloys.

The interplay between atomic ordering and magnetism in the NiPt and the CoPt systems is investigated theoretically and experimentally. The complete equilibrium phase diagrams are calculated within the framework of statistical models and are compared with experimental data. Experimental results for the Curie temperature, magnetization and paramagnetic susceptibility in ordered and disordered states are satisfactorily reproduced by a Hamiltonian that contains chemical and short-range order dependent magnetic interactions.

The phase stability of non magnetic Cu-Ni alloys is studied within a tight binding framework. Densities of states, enthalpies of mixing and ultimately the phase diagram are computed and compared to experimental data.

The phase stability of fcc-based Ni-V substitutional alloys is investigated using linear muffin-tin orbitals total energy (LMTO) calculations. The method of Connolly and Williams (CWM) is used to extract many body interactions from the ground state energies of selected ordered configurations. These interactions are used in conjunction with the cluster variation method (CVM) to calculate the alloy phase diagram. The dependence of the interactions on the choice of configurations used to calculate them is examined.

Recently, the phase diagram of AI-Li alloys was calculated with the use of the Connolly-Williams method. In an effort to test the validity and to supplement the results of that study, equilibrium lattice constants and effective cluster interactions have been obtained using the generalized perturbation method within the first-principles multiple-scattering formalism of the Korringa-Kohn-Rostoker coherent-potential approximation. The implication of these effective interactions to the phase stability of these alloys is discussed.

The phase stability of Ti-V and Ti-Cr alloys is examined within the context of an electronic structure description. Energies of mixing, effective pair interactions, and phase diagrams are computed and compared to available experimental data. A metastable distorted B2 type of structure is predicted in near equiatomic Ti-Cr.

We first discuss the applicability of the Generalized Perturbation Method to the study of ordering phenomena in complex alloys for which stability properties are electronically driven. In particular, according to previous work, it is recalled that a 3D-generalized Ising model is appropriate to address the problem of configurational order in A 15-based substitutional alloys. A ground state analysis of this model, including 1st, 2nd and weak 3rd and 7th pair interactions, generates two new ordered states at the composition A5B3 and A7B, apart from the well known A3B configuration. The stability of these predicted configurations is examined as a function of temperature and concentration by means of standard statistical techniques. The results are discussed in relation with the experimental situation.

In recent years, total energy calculations based on the local density approximation (LDA) have begun to find applications in materials science [1]. In the context of the present symposium, the most relevant application is to the calculation of total and relative energies of ordered alloy phases and their mixing enthalpies. The first-principles LDA approach is now taking over from tight-binding or simple empirical schemes in providing input to phase diagram calculations, for example, using Connolly-Williams inversion [2]. We wish to make two points in our contribution to the symposium.

It has been established that the coherent potential approximation can successfully describe the energy of random alloys [1]. It has also served as the basis of generalized perturbation method [2] and concentration wave [3] xscalculations of the energy of short range ordered alloys. The multisublattice coherent potential, (MCPA) is the natural extension of the CPA with which to address long range order (LRO). Using the recently developed multisublattice coherent potential approximation Korringa Kohn Rostoker [4], (MCPA-KKR) code the elgenvalue sum can be calculated as a function of LRO. This allows the evaluation of the ordering energy by either of two approximations. The frozen potential approximation (FPA) [5] assumes that the muffintin single site potentials do not change as the long range order is varied; the Harris Approximation, (HA) [6], as applied in this work, assumes that the single site charge densities do not change as the long range order is changed. These two methods of calculating the ordering energy will be compared with each other and to experiment for several systems including CuZn, NiAl, and NiAl with zinc additions.

Transition metal alloys are interesting in order to test statistical model based on the Ising Hamiltonian to describe order-disorder phenomena. In the case of such alloys electronic structure calculations all agree that short-ranged pairwise interactions are sufficient to account for phase diagrams and order-disorder properties in general.

The Wagner-Schottky model was used to describe the thermodynamic behavior of ordered intermetallic compound phases. To demonstrate the utility of the approach, the models developed for triple-defect B2 (and B32) and anti-structure L10 phases were used to describe the thermodynamic properties of β-AlLi and γ-TiAl respectively. Since any potential engineering materials to be developed on the basis of intermetallics will be multi-component systems, the methodology was extended to describe the thermodynamic properties of ternary intermetallics. The ternary Ti-Mo-Al system was used as an example for discussion. It is believed that the general topologies concerning the phase equilibria of Ti-M-AI with M being V, Nb, Ta, Mo and W are similar. The relative stabilities of the competing phases, i.e. BCC and HCP, in the mid-composition region of Ti-M-AI were discussed.

A liquidus projection of the Al-rich Al-Li-Cu system is proposed. The proposed liquidus projection was based on DTA, X-ray diffraction, metallography, EPMA, SEM, and chemical analysis of 50 ternary alloys. Using these data and those reported in the literature, and thermodynamic models of Al-Li, AI-Cu and Cu-Li, a thermodynamic description of the Al-rich AI-Li-Cu system was developed. The calculated isothermal sections at several temperatures and the liquidus projection are in agreement with the experimental determinations. Combining the thermodynamic models and a Scheil-type equation, quantitative solidification paths were described. The calculated amount of primary solidification phase was compared to the experimental determination.