A. Arya

Effect of chromium addition on the ordering behaviour of Ni–Mo alloy: experimental results vs. electronic structure calculations

Abstract The ordering behaviour of a Ni-Mo alloy in the presence of a ternary additive, viz. Cr, has been studied. The sequence of ordering transformations in binary Ni–Mo alloys has been shown earlier to be controlled by a competition between several f.c.c.-based superlattices, viz. Ni 2 Mo (Pt 2 Mo type), Ni 3 Mo (DO 22 ), Ni 4 Mo (D1 a ) and the so-called short range ordered (SRO) structure characterized by the presence of diffraction intensity maxima at the 1 1 / 2 0 f.c.c. positions in reciprocal space. The effect of ternary addition of chromium in the selection of the superlattice structure has been examined in this paper in an alloy of composition Ni–24 at.% Mo–6 at.% Cr. The presence of Cr has been experimentally found to favour the formation of Ni 2 (Mo,Cr) (Pt 2 Mo-type) phase in preference to the Ni 3 Mo (DO 22 ) and Ni 4 Mo (D1 a ) superlattices. This leads to a sequence of transformation different from that obtained in binary alloys. The effect of Cr on the ground state phase stability is determined, in this alloy, using the first-principles local-density based full-potential augmented plane wave (FP-LAPW) method. From the differences in the electronic structures, densities of states and total energies of binary Ni 2 Cr, Ni 2 Mo (Pt 2 Mo type), Ni 3 Mo (DO 22 ) and Ni 4 Mo (D1 a ) phases and the corresponding ternary superlattice structures, an attempt has been made to predict the hierarchy of relative phase stabilities. Theoretical predictions based on these electronic structure calculations have been found to be consistent with the experimental microstructural observations of the evolutionary stages of ordering in the ternary Ni–24 at.% Mo–6 at.% Cr alloy.

A first-principles thermodynamic approach to ordering in Ni-Mo alloys

There is a competition between several face centered cubic (FCC)-based ordered inter-metallic phases in Ni-Mo alloys containing 8-33 at% Mo. The transformation behavior of these alloys in terms of ordering instabilities has been studied. First-principles tight-binding-linear muffin-tin orbital (TB-LMTO) method coupled with augmented space recursion (ASR) in conjunction with orbital peeling (OP) technique has been employed to extract the concentration dependent effective pair interactions. Further, the mean-field statistical mechanics based static concentration wave (SCW) model has been used to determine the free energies of these ordered phases as functions of temperature, composition and order parameter. This ASR-OP-SCW approach, applied to Ni-Mo alloy system, gives the correct ground state stability sequence as observed experimentally. Furthermore, it has been shown that such an approach can be used to study the complex transformation behavior involving several competing superstructures as well as competing first order and second order ordering processes.

Ground state structural stability of ordered fcc- and bcc-based LiAl compounds under first and second nearest-neighbour pair approximation

Abstract Self-consistent local density electronic structure calculations have been performed on a series of ground state ordered superstructures of lithium-aluminium alloys spanning the entire concentration range. These structures are based on both fcc and bcc lattices under the first and second nearest neighbour pair approximation which is adequate to stabilize all the stable and metastable phases of the Liue5f8Al system. Using the efficient tight-binding linear muffin-tin orbital (TB-LMTO) method, we have calculated the volume dependent total ground state energies and the systematic trends in various cohesive and electronic properties at zero temperature, as a function of Li concentration. The predicted heats of formation for all the different ground state superstructures result in a representative stability profile, which shows that the L1 2 , B32 and DO 3 structures are the most stable amongst various phases having Al 3 Li, AlLi and AlLi 3 compositions, respectively. Moreover, we have parameterized the cohesive energies using the Connolly-Williams cluster expansion method and estimated the effective many-body interactions for the fcc lattice in an octahedron-tetrahedron cluster approximation, and for the bcc lattice in an irregular tetrahedron cluster approximation. These volume dependent but configuration (as well as concentration) independent interactions coming out of the TB-LMTO-CWM approach are not only important for first principles calculation of phase diagram but are also useful for predicting the evolutionary path of ordering processes.

Formation of an ordered intermetallic phase from a disordered solid solution—A study using first-principles calculations in Al-Li alloys

Abstract The formation of the ordered L1 2 phase in Al-Li binary solid solutions has been studied using first-principles electronic structure calculations in conjunction with the static concentration wave model. The effective multisite interactions have been determined by using Connolly-Williams prescription in the tetrahedron-octahedron (TO) cluster approximation for the f.c.c. lattice. The resulting Landau plots (free energy versus order parameter) have pointed out the temperatures below which instabilities with respect to ordering develops. Free energy-composition plots have been used for identifying the positions of the phase boundaries and of the critical spinodal. The results of this theoretical investigation have been presented in the form of a phase diagram in which different instability lines have been marked.

Cohesive and electronic properties of ordered Li-Al intermetallic compounds

Self-consistent electronic structure calculations have been performed on ordered lithium-aluminium compounds using the tight-binding linear muffin-tin orbital (TBLMTO) method. The FCC-based ground-state superstructures (namely Ll2 and Ll0 structures) show some systematic trends in their cohesive and electronic properties, which are in reasonably good agreement with the available experimental data. We have also compared the density of states, band structures and total ground-state energies of equiatomic AlLi compounds, between the FCC-based Ll0 structure and the BCC-based B32 structure. While the former shows a two-dimensional metallic behaviour, the latter shows a resemblance to a tetrahedral-bonded covalent solid, and is more stable. After detailed comparison with some recent LAPW calculations, we conclude that the TBLMTO method can be used as an efficient and reasonably accurate first-principles tool for studying the phase stability and chemical bonding in ordered intermetallic compounds.

First-principles calculations of the electronic structure and phase stability of Ni-Mo alloys

Self-consistent local density electronic structure calculations have been carried out on various fcc-based ground-state ordered superstructures of alloys spanning the entire concentration range. Using the tight-binding linear muffin-tin orbital (TB-LMTO) method, we have calculated the volume-dependent total ground-state energies, and hence the different equilibrium cohesive properties, as functions of the Mo concentration. Following the `transferability prescription of Andersen and co-workers, we have estimated the potential parameters of the constituent atoms as embedded in the alloy and compared these with the corresponding charge-self-consistent parameters for the intermetallic compounds. The ground-state stability profile has been obtained for the first time for this family of Ni-Mo compounds. Moreover, we have tested the applicability of the cluster expansion method (CEM) for parametrizing the cohesive energies to estimate the volume-dependent effective cluster interactions (ECIs) under the octahedron-tetrahedron cluster approximation.

Ordering in Ni-Mo alloys—First-principles calculations versus experimental observations

An extensive amount of experimental work has been reported in the literature on the ordering behaviour of Ni-Mo alloys containing 8–33 at% of Mo, which exhibit both short-range and long-range ordering phenomena and a competition among several fcc-based long-range ordered structures. We have used local-density-based tight binding linear muffin-tin orbital (TB-LMTO) method in conjunction with ‘augmented space recursion + orbital peeling’ (ASR + OP) for the determination of ground state energies of these superstructures in terms of effective pair interactions up to the fourth nearest neighbour pairs. The ordering behaviour of the four competing fcc-based superstructures has been studied using the mean-field-based ‘static concentration wave’ (SCW) model in terms of the free energy-order parameter plots (Landau plots) and the free energy-composition plots. The instability domains with respect to concentration fluctuations, both short wavelength (ordering) and long wavelength (clustering) have been identified from these calculations. This information has been used to predict the sequence of transformation events in the Ni-Mo alloys undergoing ordering and/or clustering and the results are compared with those obtained experimentally.

Estimate of the Coulomb correlation energy in CeAg2Ge2 from inverse photoemission and high resolution photoemission spectroscopy

The occupied and the unoccupied electronic structure of CeAg2Ge2 single crystal has been studied using high resolution photoemission and inverse photoemission spectroscopy, respectively. High resolution photoemission reveals the clear signature of Ce 4f states in the occupied electronic structure which was not observed clearly in our earlier studies. The Coulomb correlation energy in this system has been determined experimentally from the position of the 4f states above and below the Fermi level. Theoretically, the correlation energy has been determined by using the first principles density functional calculations within the generalized gradient approximations taking into account the strong intra-atomic (on-site) interaction Hubbard Ueff term. The calculated valence band shows minor changes in the spectral shape with increasing Ueff due to the fact that the density of Ce 4f state is narrow in the occupied part and is hybridized with the Ce 5d, Ag 4d and Ge 4p states. On the other hand, substantial changes are observed in the spectral shape of the calculated conduction band with increasing Ueff since the density of Ce 4f state is very large in the unoccupied part, compared to other states. The estimated value of correlation energy for CeAg2Ge2 from the experiment and the theory is ≈ 4.2 eV. The resonant photoemission data are analyzed in the framework of the single-impurity Anderson model which further confirms the presence of the Coulomb correlation energy and small hybridization in this system.

Replacive ordering in alloys

Replacive ordering can occur in an alloy in a continuous mode by the development and amplification of concentration waves of appropriate wave vectors, k. Such processes known as spinodal clustering (k∼〈000〉) and spinodal ordering (k defining the relevant superlattice structure) become operative when the alloy system experiences a free energy instability with respect to the order parameter associated with the corresponding wave vector. The presence of instabilities associated with these processes has been investigated in the Al–Li system using the cluster variation approach (CVM) considering upto the octahedron–tetrahedron cluster. The interaction energy parameters were obtained from the local density based first-principles band structure calculations. Predicted instability regimes have been compared with those obtained experimentally. The development of different competing superlattice structures in the Ni–Mo system has been discussed in terms of the development of appropriate concentration waves. Free energy–order parameter plots for different k-vectors have been compared for predicting relative stabilities of these superstructures and the evolutionary path of the ordering process. These results have been shown to be consistent with the experimental findings on this system.

First-Principles Approach to Ordering and Clustering Behavior in Metallic Alloys: Application to Al-Li and Ni-Mo Systems

The thermodynamic stability/metastability/instability of an alloy system with respect to short- and long-wavelength (ordering and clustering) concentration fluctuations has been studied using the free energy models viz. the ‘static concentration wave’ model and the ‘cluster variation method’. The input to these statistical mechanics based models, viz. the effective cluster interactions, have been provided by using first-principles ‘tight-binding linear muffin-tin orbital’ method in conjunction with (a) the ‘inversion method’ and (b) the ‘augmented space recursion — orbital peeling’ technique. The above methodology has been employed to study the precipitation of δ’ — Al3Li phase from the disordered Al-Li alloys and also to study the ordering reactions in Ni-Mo alloys which involves a number of fcc-based ordered superstructures competing for precipitation.