pp 1-2
pp 3-12
Density functional theory and multiscale materials modeling
One of the vital ingredients in the theoretical tools useful in materials modeling at all the length scales of interest is the concept of density. In the microscopic length scale, it is the electron density that has played a major role in providing a deeper understanding of chemical binding in atoms, molecules and solids. In the intermediate mesoscopic length scale, an appropriate picture of the equilibrium and dynamical processes has been obtained through the single particle number density of the constituent atoms or molecules. A wide class of problems involving nanomaterials, interfacial science and soft condensed matter has been addressed using the density based theoretical formalism as well as atomistic simulation in this regime. In the macroscopic length scale, however, matter is usually treated as a continuous medium and a description using local mass density, energy density and other related density functions has been found to be quite appropriate. A unique single unified theoretical framework that emerges through the density concept at these diverse length scales and is applicable to both quantum and classical systems is the so called density functional theory (DFT) which essentially provides a vehicle to project the many-particle picture to a single particle one. Thus, the central equation for quantum DFT is a one-particle Schrödinger-like Kohn–Sham equation, while the same for classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential. Selected illustrative applications of quantum DFT to microscopic modeling of intermolecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are presented.
pp 13-17
Realization of prediction of materials properties by ab initio computer simulation
Ab initio treatment is becoming realistic to predict physical, chemical, and even mechanical properties of academically and industrially interesting materials. There is, however, some limitation in size and time of the system up to the order of several hundred atoms and ∼ 1 pico second, even if we use the fastest supercomputer efficiently. Therefore, it is very difficult to simulate realistic materials with grain boundaries and important reactions like diffusion in materials. To improve this situation, two ways have been invented. One way is to upgrade approximations to match the necessary levels according to inhomogeneous electron gas theory beyond the present day standard, i.e. local density approximation (LDA). The reason is simply that the system we are interested in is composed of many particles interacting with Coulomb forces governed by quantum mechanics. (Complete knowledge is available, and only what we should do is to make better approximations to explain the phenomena!). Another is to extract the necessary parameters from the ab initio calculations on systems with limited number of atoms, and apply these results into cluster variation, direct, or any other sophisticated methods based on classical concepts such as statistical mechanics.
In this paper, several typical examples recently worked out by our research group are introduced to indicate that these methodologies are actually possible to be successfully used to predict materials properties before experiments based on the present day state-of-art supercomputing systems. It includes scientific visualization of the results of ab initio molecular dynamics simulation on atom insertion process to C_{60} and to carbon nanotube, tight-binding calculation of single electron conductance properties in nanotube to create nano-scale diode virtually by computer, which will be a base of future nanoscale electric device in nanometer size, Li + H reaction without Born–Oppenheimer approximation, structural phase transitions in perovskite materials under very high pressure in earth by direct method, and prediction of wavelength of emitted light from Na clusters with GW (G = Green function-vertex, W = screened Coulomb interaction) approximation.
pp 19-26
Third-generation muffin–tin orbitals
O K Andersen T Saha-Dasgupta S Ezhov
By the example of $sp^3$-bonded semiconductors, we illustrate what 3rd-generation muffin–tin orbitals (MTOs) are. We demonstrate that they can be downfolded to smaller and smaller basis sets: $sp^3d^{10}, sp^3$, and bond orbitals. For isolated bands, it is possible to generate Wannier functions a priori. Also for bands, which overlap other bands, Wannier-like MTOs can be generated a priori. Hence, MTOs have a unique capability for providing chemical understanding.
pp 27-32
Tight-binding model for carbon from the third-generation LMTO method: A study of transferability
D Nguyen-Manh T Saha-Dasgupta O K Andersen
The third-generation LMTO method provides a new wave function basis set in which the energy dependence of the interstitial region and inside muffin–tin (MT) spheres is treated on an equal footing. Within the improved method, basis functions in the interstitial are the screened spherical waves (SSWs) with boundary condition defined in terms of a set of ‘hard’ sphere radii $a_{RL}$. Energy eigenvalues obtained from the singleparticle Schrödinger equation for MT potential is energetically accurate and very useful for predicting a reliable first-principles tight-binding (TB) model of widely different systems. In this study, we investigate a possibility of the new basis sets transferability to different environment which could be crucial for TB applications to very large and complicated systems in realistic materials modelling. For the case of C where the issue of $sp^2$ vs $sp^3$ bonding description is primarily important, we have found that by downfolding the unwanted channels in the basis, the TB electronic structure calculations in both hexagonal graphite and diamond structures are well compared with those obtained from the full LDA schemes if we use the same choice of hard sphere radii, aRL and a fixed, arbitrary energy, 𝜀_{𝜈}. Moreover, the choice is robust and transferable to various situations, from different forms of graphite to a wide range of coordination. Using the obtained minimal basis set, we have been investigating the TB Hamiltonian and overlap matrices for different structure types for carbon, in particular we have predicted the on-site and hopping parameters (𝛾_{1}, 𝛾_{2}, $\cdots$, 𝛾_{6}) within an orthogonal representation for Slonczewski–Weiss–McClure (SWMcC) model of the Bernal structure. Our theoretical values are in excellent agreement with experimental ones from magnetoreflection measurements of Fermi surfaces for hexagonal graphite.
pp 33-41
Projector augmented wave method: ab initio molecular dynamics with full wave functions
Peter E Blöchl Clemens J Först Johannes Schimpl
A brief introduction to the projector augmented wave method is given and recent developments are reviewed. The projector augmented wave method is an all-electron method for efficient ab initio molecular dynamics simulations with full wave functions. It extends and combines the traditions of existing augmented wave methods and the pseudopotential approach. Without sacrificing efficiency, the PAW method avoids transferability problems of the pseudopotential approach and it has been valuable to predict properties that depend on the full wave functions.
pp 43-51
Environmentally dependent bond-order potentials: New developments and applications
D Nguyen-Manh D G Pettifor D J H Cockayne M Mrovec S Znam V Vitek
The bond-order potentials (BOPs) idea employs the orthogonal two-centre tight-binding (TB) representation for the bond energy and the Harris–Foulkes approximation for the repulsive pairwise contribution. In the last ten years, although many efforts have been focused on theoretical calculations of the bond order expression, the BOPs still suffers from the uncertainty of how best to choose the semi-empirical TB parameters that enter the scheme. In this paper, we review recent developments to obtain the reliable and transferable BOPs which help to extend the accuracy and applicability to technologically important multicomponent systems. Firstly, we have found that a simple pair potential is unsuitable for describing the environmental screening effects due to the 𝑠 and 𝑝 orbital overlap repulsion in transition metal alloys and therefore the inability to reproduce the negative Cauchy pressures exhibiting in strong covalent systems. By adding the environmental dependent repulsive term, the Cauchy pressure problem has been removed and we are now able to get the BOPs for studying dislocations, extended defects and mechanical properties of hightemperature intermetallic Ti–Al alloys. In particular, new results on the core structures and possible dissociation of different type of dislocations will be discussed. Secondly, we present the first derivation of explicit analytic expressions for environmental dependence of 𝜎, 𝜋 and 𝛿 bond integrals by inverting the non-orthogonal matrix. We illustrate the power of this new formalism by showing that it not only captures the transferability of bond integrals between Mo, Si and MoSi_{2} but also predicts the large discontinuities between first and second nearest neighbours for $pp\sigma, pp\pi$ and $dd\pi$ even though absence of any discontinuity for the $dd\sigma$ bond integral. A new environmentally dependent BOPs has been developed for bcc-Mo indicating that the core structure of 1/2$\langle$111$\rangle$ screw dislocations is narrower than structures found in previous studies in agreement with recent ab initio calculations. Finally, the new formalism will allow us to study the problem of medium range order found recently in amorphous materials with covalent bonding at large and realistic nanoscale. For the case of 𝑎-C where the issue of $sp^2$ vs $sp^3$ is very crucial for modelling amorphous structure we found that the 𝜎 and 𝜋 bond integrals are not only transferable between graphite and diamond structures but they are also strongly anisotropic due to inter-plan bonding between graphite sheets.
pp 53-62
Multi-scale modeling strategies in materials science—The quasicontinuum method
The problem of prediction of finite temperature properties of materials poses great computational challenges. The computational treatment of the multitude of length and time scales involved in determining macroscopic properties has been attempted by several workers with varying degrees of success. This paper will review the recently developed quasicontinuum method which is an attempt to bridge the length scales in a single seamless model with the aid of the finite element method. Attempts to generalize this method to finite temperatures will be outlined.
pp 63-67
Many electron effects in semiconductor quantum dots
R K Pandey Manoj K Harbola V Ranjan Vijay A Singh
Semiconductor quantum dots (QDs) exhibit shell structures, very similar to atoms. Termed as ‘artificial atoms’ by some, they are much larger (1 100 nm) than real atoms. One can study a variety of manyelectron effects in them, which are otherwise difficult to observe in a real atom. We have treated these effects within the local density approximation (LDA) and the Harbola–Sahni (HS) scheme. HS is free of the selfinteraction error of the LDA. Our calculations have been performed in a three-dimensional quantum dot. We have carried out a study of the size and shape dependence of the level spacing. Scaling laws for the Hubbard ‘𝑈’ are established.
pp 69-74
Obtaining Kohn–Sham potential without taking the functional derivative
Over the past decade and a half, many new accurate density functionals, based on the generalized gradient approximation, have been proposed, and they give energies close to chemical accuracy. However, accuracy of the energy functional does not guarantee that its functional derivative, which gives the corresponding potential, is also accurate all over space. For example, although the Becke88 exchange–energy functional gives very good exchange energies, its functional derivative goes as $-\frac{1}{r^2}$ in comparison to the correct $-\frac{1}{r}$ for $r \rightarrow \infty$, where 𝑟 is the distance of the electron from a finite system. On the other hand, accuracy of the potential is of prime importance if one is interested in properties other than the total energy; properties such as optical response depend crucially on the potential in the outer regions of a system. In this paper we present a different approach, based on the ideas of Harbola and Sahni, to obtain the potential directly from the energy density of a given approximation, without taking recourse to the functional derivative route. This leads to a potential that is as accurate as the functional itself. We demonstrate the accuracy of our approach by presenting some results obtained from the Becke88 functional.
pp 75-78
Exchange–correlation errors at harmonic and anharmonic orders: the case of bulk Cu
Shobhana Narasimhan Stefano De Gironcoli
As an aid towards improving the treatment of exchange and correlation effects in electronic structure calculations, it is desirable to have a clear picture of the errors introduced by currently popular approximate exchange–correlation functionals. We have performed ab initio density functional theory and density functional perturbation theory calculations to investigate the thermal properties of bulk Cu, using both the local density approximation (LDA) and the generalized gradient approximation (GGA). Thermal effects are treated within the quasiharmonic approximation. We find that the LDA and GGA errors for anharmonic quantities are an order of magnitude smaller than for harmonic quantities; we argue that this might be a general feature. We also obtain much closer agreement with experiment than earlier, more approximate calculations.
pp 79-89
A first-principles thermodynamic approach to ordering in binary alloys
Abhijit mookerjee Tanusri Saha-Dasgupta I Dasgupta A Arya S Banerjee G P Das
The communication reviews the augmented space based approaches to thermodynamics and ordering of binary alloys. We give several examples of metallic alloys to illustrate our methodology.
pp 91-96
Double stripe reconstruction of the Pt(111) surface
Raghani Pushpa Shobhana Narasimhan
We have studied the reconstruction of the Pt(111) surface theoretically, using a 2D generalization of the Frenkel–Kontorova model. The parameters in the model are obtained by performing ab initio density functional theory calculations. The Pt(111) surface does not reconstruct under normal conditions but experiments have shown that there are two ways to induce the reconstruction: by increasing the temperature, or by depositing adatoms on the surface. The basic motif of this reconstruction is a `double stripe’ with an increased surface density and alternating hcp and fcc domains, arranged to form a honeycomb pattern with a very large repeat distance of 100–300 Å. In this paper, we have studied the `double stripe’ reconstruction of the Pt(111) surface. In agreement with experiment, we find that it is favourable for the surface to reconstruct in the presence of adatoms, but not otherwise.
pp 97-103
Site preference of Zr in Ti_{3}Al and phase stability of Ti_{2}ZrAl
The site preference of Zr atoms in Ti_{3}Al and the phase stability of Ti_{2}ZrAl are examined using first-principles electronic structure total energy calculations. Of the sixteen possible ways in which Ti, Zr and Al atoms can be arranged, in the lattice sites corresponding to $D0_{19}$ structure of Ti_{3}Al, to obtain Ti_{2}ZrAl, it is s hown that Zr atoms prefer to get substituted at the Ti sites. It is further shown that among the seven crystal structures considered, $D0_{19}$-like and $L1_2$-like are the competing ground-state structures of Ti_{2}ZrAl. The above results are in agreement with the experimental results reported in the literature. Calculated values of equilibrium lattice parameters, heat of formation and bulk modulus of Ti_{2}ZrAl are presented. The basis for the structural stability and bonding are analysed in terms of the density of states. Between the two possible 𝐵2-like structures, Ti_{2}ZrAl shows enhanced stability for the one where Zr is substituted in the Ti sublattice, which again is in agreement with the experimental observation.
pp 105-107
Electronic properties of magnetically doped nanotubes
Keivan Esfarjani Z Chen Y Kawazoe
Effect of doping of carbon nanotubes by magnetic transition metal atoms has been considered in this paper. In the case of semiconducting tubes, it was found that the system has zero magnetization, whereas in metallic tubes the valence electrons of the tube screen the magnetization of the dopants: the coupling to the tube is usually antiferromagnetic (except for Cr).
pp 109-114
Novel caged clusters of silicon: Fullerenes, Frank–Kasper polyhedron and cubic
We review recent findings of metal (M) encapsulated caged clusters of Si and Ge obtained from computer experiments based on an ab initio pseudopotential method. It is shown that one M atom changes drastically the properties of Si and Ge clusters and that depending upon the size of the M atom, cages of 14, 15, and 16 Si as well as Ge atoms are formed. In particular M@Si_{16} silicon fullerene has been obtained for M = Zr and Hf, while a Frank–Kasper polyhedron has been obtained for M@X_{16}, X = Si and Ge. These clusters show high stability and large highest occupied–lowest unoccupied molecular orbital (HOMO–LUMO) gaps which are likely to make these species strongly abundant. A regular icosahedral M@X_{12} cluster has also been obtained for X = Ge and Sn by doping a divalent M atom. Interactions between clusters are rather weak. This is attractive for developing self-assembled cluster materials.
pp 115-116
Tina M Briere Marcel H F Sluiter Vijay Kumar Yoshiyuki Kawazoe
The geometries of several Mn clusters in the size range Mn_{13}–Mn_{23} are studied via the generalized gradient approximation to density functional theory. For the 13- and 19-atom clusters, the icosahedral structures are found to be most stable, while for the 15-atom cluster, the bcc structure is more favoured. The clusters show ferrimagnetic spin configurations.
pp 117-121
Ground state structures and properties of small hydrogenated silicon clusters
We present results for ground state structures and properties of small hydrogenated silicon clusters using the Car–Parrinello molecular dynamics with simulated annealing. We discuss the nature of bonding of hydrogen in these clusters. We find that hydrogen can form a bridge like Si–H–Si bond connecting two silicon atoms. We find that in the case of a compact and closed silicon cluster hydrogen bonds to the silicon cluster from outside. To understand the structural evolutions and properties of silicon cluster due to hydrogenation, we have studied the cohesive energy and first excited electronic level gap of clusters as a function of hydrogenation. We find that first excited electronic level gap of Si_{𝑛} and Si_{𝑛}H fluctuates as function of size and this may provide a first principle basis for the short-range potential fluctuations in hydrogenated amorphous silicon. The stability of hydrogenated silicon clusters is also discussed.
pp 123-125
Ground state structures and properties of Si_{3}H_{𝑛} (𝑛 = 1–6) clusters
The ground state structures and properties of Si_{3}H_{𝑛} (1 ≤ 𝑛 ≤ 6) clusters have been calculated using Car–Parrinello molecular dynamics with simulated annealing and steepest descent optimization methods. We have studied cohesive energy per particle and first excited electronic level gap of the clusters as a function of hydrogenation. Hydrogenation is done till all dangling bonds of silicon are saturated. Our results show that over coordination of hydrogen is favoured in Si_{3}H_{𝑛} clusters and the geometry of Si_{3} cluster does not change due to hydrogenation. Cohesive energy per particle and first excited electronic level gap study of the clusters show that Si_{3}H_{6} cluster is most stable and Si_{3}H_{3} cluster is most unstable among the clusters considered here.
pp 127-130
Application of genetic algorithms to hydrogenated silicon clusters
We discuss the application of biologically inspired genetic algorithms to determine the ground state structures of a number of Si–H clusters. The total energy of a given configuration of a cluster has been obtained by using a non-orthogonal tight-binding model and the energy minimization has been carried out by using genetic algorithms and their recent variant differential evolution. Our results for ground state structures and cohesive energies for Si–H clusters are in good agreement with the earlier work conducted using the simulated annealing technique. We find that the results obtained by genetic algorithms turn out to be comparable and often better than the results obtained by the simulated annealing technique.
pp 131-135
Theoretical study of superconductivity in MgB_{2} and its alloys
Using density-functional-based methods, we have studied the fully-relaxed, full-potential electronic structure of the newly discovered superconductor, MgB_{2}, and BeB_{2}, NaB_{2} and AlB_{2}. Our results, described in terms of
For BeB_{2} and NaB_{2}, our results indicate qualitative similarities but significant quantitative differences in their electronic structure due to differences in the number of valence electrons and the lattice constants 𝑎 and 𝑐.
We have also studied Mg_{1-𝑥}M_{𝑥}B_{2} ((M ≡ Al), Li or Zn) alloys using coherent-potential to describe disorder, Gaspari–Gyorffy approach to evaluate electron–phonon coupling, and Allen–Dynes equation to calculate the superconducting transition temperature, $T_c$. We find that in Mg_{1-𝑥}M_{𝑥}B_{2} alloys
pp 137-141
Electronic structure and superconductivity of MgB_{2}
D M Gaitonde P Modak R S Rao B K Godwal
Results of ab initio electronic structure calculations on the compound, MgB_{2}, using the FPLAPW method employing GGA for the exchange–correlation energy are presented. Total energy minimization enables us to estimate the equilibrium volume, 𝑐/𝑎 ratio and the bulk modulus, all of which are in excellent agreement with experiment. We obtain the mass enhancement parameter by using our calculated, $D(E_F)$ and the experimental specific heat data. The $T_c$ is found to be 37 K. We use a parametrized description of the calculated band structure to obtain the 𝑇 = 0 K values of the London penetration depth and the superconducting coherence length. The penetration depth calculated by us is too small and the coherence length too large as compared to the experimentally determined values of these quantities. This indicates the limitations of a theory that relies only on electronic structure calculations in describing the superconducting state in this material and implies that impurity effects as well as mass renormalization effects need to be included.
pp 143-146
Oscillatory interlayer magnetic coupling and induced magnetism in Fe/Nb multilayers
We present an ab initio calculation of interlayer magnetic coupling for Fe/Nb multilayers using the self-consistent full-potential linearized augmented-plane-wave (FLAPW) method. For this calculation, we have constructed supercells consisting of bcc Fe and Nb multilayers in Fe/Nb/Fe sandwich geometry stacked along (001) direction. In the supercells two Fe layers are separated by Nb layers ranging from 1 to 11 layers. We have calculated the total energy of the system as a function of Nb spacer layer thickness. For each spacer layer thickness, we have done three calculations corresponding to para, ferro and antiferromagnetic ordering of Fe atoms. The interlayer magnetic coupling is obtained from the energy difference of the systems in which Fe layers are antiferromagnetically and ferromagnetically ordered. We find that the interlayer magnetic coupling oscillates with increasing Nb spacer thickness in agreement with the experimental results. The induced magnetic moment is also found to be oscillating with increasing Nb spacer layer thickness.
pp 147-150
Effect of Co on the magnetism and phase stability of lithiated manganese oxides
R Prasad R Benedek M M Thackeray
We present first-principles calculations of the relative energies of various phases of lithiated manganese oxides with and without Co. We use the ultrasoft pseudopotential method as implemented in the Vienna ab initio simulation package (VASP). The calculations employ the local spin density approximation (LSDA) as well as the generalized gradient approximation (GGA). We consider monoclinic and rhombohedral structures in paramagnetic, ferromagnetic and antiferromagnetic (AF3) spin configurations. Spinpolarization significantly lowers the total energy in all cases. The effect of Co on the stability of these phases is discussed.
pp 151-154
B T Cong P N A Huy N H Long D D Long
The reentrant magnetic phase transition in Pr_{0.5}Sr_{0.41}Ca_{0.09}MnO_{3} perovskite is explained using the Ising spin model on the square lattice with mixed ferromagnetic and antiferromagnetic exchange interactions. It is shown using numerical calculations that this effect is strongly affected by the external magnetic field and lattice disorder.
pp 155-158
Total energy calculation of perovskite, BaTiO_{3}, by self-consistent tight binding method
B T Cong P N A Huy P K Schelling J W Halley
We present results of numerical computation on some characteristics of BaTiO_{3} such as total energy, lattice constant, density of states, band structure etc using self-consistent tight binding method. Besides strong Ti–O bond between 3𝑑 on titanium and 2𝑝 orbital on oxygen states, we also include weak hybridization between the Ba 6𝑠 and O 2𝑝 states. The results are compared with those of other more sophisticated methods.
pp 159-163
Linear and nonlinear optical properties of borate crystals as calculated from the first principles
With the development of the state-of-the-art band calculation scheme and massively parallel processing in the high performance computing, we are now able to calculate all important physical properties, including
from the first principles for complex practical nonlinear optical crystals, such as the borate crystal series, with an accuracy acceptable for materials development/design, and answer the questions often raised by the material scientists.
pp 165-168
Electronic structure and optical properties of thorium monopnictides
We have calculated the electronic density of states (DOS) and dielectric function for the ThX (X = P, As and Sb) using the linear muffin tin orbital method within atomic sphere approximation (LMTO–ASA) including the combined correction terms. The calculated electronic DOS of ThSb has been compared with the available experimental data and we find a good agreement. The calculated optical conductivity for ThP and ThAs is increasing monotonically, while for ThSb a sharp peak has been found at 6.5 eV. Unfortunately there are no experimental data to compare with calculated optical properties, we hope our calculations will motivate some experimentalists.
pp 169-173
There is an abundant literature on calculations of formation and ionization energies of point defects in GaAs. Since most of these energies, especially the formation energies, are difficult to measure, the calculations are primary means of obtaining their values. However, based on the assumptions of the calculations, the reported values differ greatly among the various calculations. In this paper we discuss the sources of errors and their impact on practical predictions valuable in GaAs device fabrication. In particular, we have compared a large set of computed energies and selected the most appropriate values. Then, in the context of GaAs material quality, we investigated the impact of errors in calculation of formation energies on the performance of the GaAs substrate for device fabrication. We find that in spite of the errors inherent in ab initio calculations, it is possible to correctly predict the behaviour of GaAs substrate.
pp 175-181
On the electronic structure and equation of state in high pressure studies of solids
We discuss the high pressure behaviour of zinc as an interesting example of controversy, and of extensive interplay between theory and experiment. We present its room temperature electronic structure calculations to study the temperature effect on the occurrence of its controversial axial ratio (𝑐/𝑎) anomaly under pressure, and the related electronic topological transition (ETT). We have employed a dense 63 × 63 × 29 k-point sampling of the Brillouin zone and find that the small (𝑐/𝑎) anomaly near 10 GPa pressure persists at room temperature. A weak signature of the anomaly can be seen in the pressure–volume curve, which gets enhanced in the universal equation of state, along with that of 𝐾-point ETTs. We attribute the change of slope in the universal equation of state near 10 GPa pressure, mainly to hybridization effects. The temperature effect in fact enhances the possibility of 𝐿-point ETT. We find that the 𝐿-point ETT is very sensitive to exchange correlation terms, and hence we suggest that further refinements in the theoretical techniques are needed to resolve the controversies on the ETT in Zn.
pp 183-187
On the stability of rhenium up to 1 TPa pressure against transition to the bcc structure
A K Verma P Ravindran R S Rao B K Godwal R Jeanloz
We have carried out electronic structure total energy calculations on rhenium in the hexagonal close packed (hcp) and body centred cubic (bcc) phases, by the full potential linear muffin–tin orbital method, in order to verify the stability of the ambient pressure hcp phase against transition to the bcc structure at high pressures. As per our results, no hcp to bcc structural transition can occur up to 1 TPa pressures. Moreover, our Bain path calculations show that face centred cubic and body centred tetragonal structures are also not energetically preferred over hcp in this pressure range. The axial ratio (𝑐/𝑎) of Re changes by less than 0.33% in the pressure range studied.
pp 189-192
Spinodal decomposition in fine grained materials
We have used a phase field model to study spinodal decomposition in polycrystalline materials in which the grain size is of the same order of magnitude as the characteristic decomposition wavelength ($\lambda_{SD}$). In the spirit of phase field models, each grain (𝑖) in our model has an order parameter ($\eta_i$) associated with it; $\eta_i$ has a value of unity inside the 𝑖th grain, decreases smoothly through the grain boundary region to zero outside the grain. For a symmetric alloy of composition, 𝑐 = 0.5, our results show that microstructural evolution depends largely on the difference in the grain boundary energies, $\gamma_{gb}$, of A-rich (𝛼) and B-rich (𝛽) phases. If $\gamma^{\alpha}_{gb}$ is lower, we find that the decomposition process is initiated with an 𝛼 layer being formed at the grain boundary. If the grain size is sufficiently small (about the same as $\lambda_{SD}$), the interior of the grain is filled with the 𝛽 phase. If the grain size is large (say, about 10 $\lambda_{SD}$ or greater), the early stage microstructure exhibits an A-rich grain boundary layer followed by a B-rich layer; the grain interior exhibits a spinodally decomposed microstructure, evolving slowly. Further, grain growth is suppressed completely during the decomposition process.
pp 193-197
A study of phase separation in ternary alloys
Saswata Bhattacharyya T A Abinandanan
We have studied the evolution of microstructure when a disordered ternary alloy is quenched into a ternary miscibility gap. We have used computer simulations based on multicomponent Cahn–Hilliard (CH) equations for 𝑐_{A} and 𝑐_{B}, the compositions (in mole fraction) of A and B, respectively. In this work, we present our results on the effect of relative interfacial energies on the temporal evolution of morphologies during spinodal phase separation of an alloy with average composition, 𝑐_{A} = 1/4, 𝑐_{B} = 1/4 and 𝑐_{A} = 1/2. Interfacial energies between the ‘A’ rich, ‘B’ rich and ‘C’ rich phases are varied by changing the gradient energy coefficients. The phases associated with a higher interfacial energy are found to be more rounded than those with lower energy. Further, the kinetic paths (i.e. the history of A-rich, B-rich and C-rich regions in the microstructure) are also affected significantly by the relative interfacial energies of the three phases.
pp 199-205
Ashish Bhattacharjee Mesbahuddin Ahmed Abhijit Mookerjee Amal Halder
We use the self-consistent, augmented space recursion technique to study the electronic structure and magnetic properties of alloys of the transition metals, Fe, Co and Ni with the noble metals, Ag and Au. We analyse the effect of local environment and the hybridization between the constituent bands on the electronic and magnetic properties.
Current Issue
Volume 41 | Issue 5
October 2018
© 2017 Indian Academy of Sciences, Bengaluru.