Theory of alloys. II. Embedded-cluster calculations of phonon spectra for a one-dimensional ternary alloy (original) (raw)
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Physical Review B, 2004
We present here an augmented space recursive technique in the k-representation which include diagonal, off-diagonal and the environmental disorder explicitly : an analytic , translationally invariant , multiple scattering theory for phonons in random binary alloys. We propose the augmented space recursion (ASR) as a computationally fast and accurate technique which will incorporate configuration fluctuations over a large local environment. We apply the formalism to N i55P d45 , N i88Cr12 and N i50P t50 alloys which is not a random choice. Numerical results on spectral functions, coherent structure factors, dispersion curves and disordered induced FWHM's are presented. Finally the results are compared with the recent itinerant coherent potential approximation (ICPA) and also with experiments.
Cluster densities of states of nonrandom substitutionally disordered alloys
Physical Review B, 1984
The embedded-cluster method is used to calculate the density of states (DOS) of nonrandom substitutionally disordered alloys. This method is based on the calculation of the Green's function for a cluster of atoms embedded in an effective medium. The effect of increasing cluster size as well as of different choices of the effective medium is investigated numerically in terms of one-dimensional alloys with various scattering strengths and degrees of short-range-order (SRO). A method for the self-consistent treatment of SRO in terms of the pair distribution function is proposed and in many cases is found to lead to results in much better agreement with exact DOS's than those obtained when SRO is not treated self-consistently.
Unification of the phonon mode behavior in semiconductor alloys: Theory andab initiocalculations
Physical Review B, 2008
We demonstrate how to overcome serious problems in understanding and classification of vibration spectra in semiconductor alloys, following from traditional use of the virtual crystal approximation (VCA). We show that such different systems as InGaAs (1-bond→1-mode behavior), InGaP (modified 2-mode) and ZnTeSe (2-bond→1-mode) obey in fact the same phonon mode behavior-hence probably a universal one-of a percolation-type (1-bond→2-mode). The change of paradigm from the 'VCA insight' (an averaged microscopic one) to the 'percolation insight' (a mesoscopic one) offers a promising link towards the understanding of alloy disorder. The discussion is supported by ab initio simulation of the phonon density of states at the zone-center of representative supercells at intermediary composition (ZnTeSe) and at the impurity-dilute limits (all systems). In particular, we propose a simple ab initio 'protocol' to estimate the basic input parameters of our semi-empirical 'percolation' model for the calculation of the 1-bond→2-mode vibration spectra of zincblende alloys. With this, the model turns self-sufficient.
Self-consistent cluster theories for alloys with diagonal and off-diagonal disorder
Physical Review B, 1978
The molecular coherent-potential approximation (MCPA) and other, simpler cluster approximations for disordered alloys are studied both analytically and numerically for alloys with diagonal and off-diagonal disorder (ODD). First, the MCPA for alloys with only diagonal disorder is rederived within the interactor formalism of Blackman, Esterling, and Berk. This formalism, which simplifies the numerical implementation of the MCPA, is then used to generalize the MCPA so as to take account of ODD. It is shown that the analytic properties of the MCPA are preserved under this generalization. Also, two computationally simple cluster approximations, the self-consistent central-site approximation (SCCSA) and the self-consistent boundary-site approximation (SCBSA), are generalized to include the effects of ODD. It is shown that for one-dimensional systems with only nearest-neighbor hopping the SCBSA yields Green s functions which are identical to those given by the MCPA and thus are analytic, even in the presence of ODD. Finally, the results of numerical calculations are reported for one-dimensional systems with only nearest-neighbor hopping but with both diagonal and off-diagonal disorder. These calculations were performed using the single-site approximation of Blackman, Esterling, and Berk and three different cluster approximationsthe multishell method previously proposed by the authors, the SCCSA, and the SCBSA. The results of these calculations are compared with. exact results and with previous results obtained using the truncated-t-matix approximation and the recent method of Kaplan and Gray. These comparisons suggest that the multishell method and the generalization of the SCBSA given in this paper are more efficient and accurate for the calculation of densities of states for systems with ODD. On the other hand, as expected, the SCCSA was found to yield severely nonanalytic results for the values of band parameters used.
Physical Review B, 1990
A self-consistent cluster theory, the Korringa-Kohn-Rostoker cluster coherent-potential approximation (KKR-CCPA), is presented to study the electronic structure of the random, substitutionally disordered metallic alloys. This theory combines the augmented-space formalism and conventional Korringa-Kohn-Rostoker methods to determine the effective medium self-consistently. One advantage of this method is that it preserves Herglotz properties of the configuration-averaged Green's function needed to calculate various electronic properties, such as charge densities, essential for full charge self-consistency. Unlike the single-site approximations, the KKR-CCPA introduces diagonal as well as off-diagonal corrections in the scattering matrices. The formulation has been applied to a model one-dimensional alloy. We find that the density of states in the KKR-CCPA is somewhat structured, due to correlated scattering from clusters of atoms.
Physical Review B, 2007
A first principles density functional based linear response theory (the so called Density Functional Perturbation theory [1]) has been combined separately with two recently developed formalism for a systematic study of the lattice dynamics in disordered binary alloys. The two formalisms are the Augmented space recursion (ASR) [2] and the Itinerant coherent potential approximation (ICPA) . The two different theories (DFPT-ASR and DFPT-ICPA) systematically provides a hierarchy of improvements upon the earlier single site based theories (like CPA etc.) and includes non-local correlations in the disorder configurations. The formalisms explicitly take into account fluctuations in masses, force constants and scattering lengths. The combination of DFPT with these formulation helps in understanding the actual interplay of force constants in alloys. We illustrate the methods by applying to a fcc Fe50Pd50 alloy. PACS numbers: 61.46.+w, 36.40.Cg, 75.50.Pp I.
Self-consistent cluster theory of disordered alloys
Physics Letters A, 1972
Several techniques for extending the single-site coherent-potential approximation (CPA) to account for particular local configurations of atoms are evaluated. It is shown that if one attempts to define a site-diagonal medium by requiring consistency between the Green's function evaluated at the center of the cluster and the external medium, one may obtain unphysical results. If, however, one requires consistency between a site at the boundary and the medium, one can obtain (at least in one dimension) a site-diagonal medium which reproduces the cellular CPA exactly.
Ab initio calculation of phonon dispersions in size-mismatched disordered alloys
Physical Review B, 2010
Size mismatch and the resulting local lattice relaxations play a very crucial role in determining the latticedynamical properties of substitutionally disordered alloys. In this paper we focus on the influence of size mismatch between the components of a disordered alloy on the phonon dispersions, by considering the illustrative examples of Cu 0.715 Pd 0.285 and Cu 0.75 Au 0.25 systems. A combination of ab initio electronic-structure method and the transferable force-constant model has been used as a first-principles tool to compute the interatomic force constants between various pairs of chemical specie in a disordered alloy. The Green'sfunction based itinerant coherent-potential approximation is then used to compute the phonon-dispersion relations by performing the configuration averaging over the fluctuations in the mass and the force constants due to the size mismatch. A systematic investigation on the influence of the size mismatch of end-point components of an alloy on the phonon spectra is carried out in detail. We show that the consideration of the local lattice relaxation as a manifestation of size mismatch is important in addressing the correct behavior of the phonon dispersions in these alloys. Our results are in good agreement with the experimental results in case of Cu 0.715 Pd 0.285 . In case of Cu 0.75 Au 0.25 , our results predict a resonance behavior which is not observed experimentally. Based upon an analysis of the interatomic force constants between various pairs of chemical specie, we explain the reason of this discrepancy.
Journal of Physics: Condensed Matter, 2011
In an attempt to obtain reliable first-principles phonon dispersions of random alloys, we have developed a method to calculate the dynamical matrix, with respect to the wavevector space of the ideal lattice, by averaging over the force constants of a special quasi-random structure. Without additional approximations beyond standard density functional theory, the present scheme takes into account the local atomic position relaxations, the composition disorder, and the force constant disorder in a random alloy. Numerical results are presented for disordered Cu 3 Au, FePd, and NiPd and good agreement between the calculations and the inelastic neutron scattering data is observed.
Impurity Modes and Effect of Clustering in Diluted Semiconductor Alloys
3rd France-Russia Seminar, 2007
The variation of TO zone-center vibration spectra with concentration in mixed zincblende-type semiconductors can be understood within a paradigm of uni ed "one bond-two modes" approach, which has been recently outlined as a rather general concept, 1 and emerges from a number of previous experimental and theoretical studies. 2,3 The crucial issue is that the vibration frequency, associated with a certain cation-anion bond, depends on the length of the latter, and the bond length, in its turn, depends not only on the average alloy concentration, but on local variations of it. In an (A,B)C substitutional alloy, the A-C bond length differ in A-rich and A-poor regions, yielding a splitting of the A-C vibration frequency. Such splittings can be measured and reproduced in rst-principles calculations. An analysis of vibration spectra helps to get an insight into the structural short-range (clustering) and long-range (formation of extended chains of certain cation-anion pairs and other structural motives at the mesoscopic scale) tendencies. For this however, one needs rstprinciples benchmark calculations for representative model systems (see, e.g., Ref. 4 for the ZnSe-BeSe alloys). The simplest yet important result from rst-principles calculations is a prediction of how the impurity phonon mode evolves as isolated (distant) impurities get clustered. In the present contribution, we outline the results of rst-principles calculations of phonon frequencies and vibration patterns, in the dilution limits of several mixed semiconductor alloys, Be x Zn 1−x Se, Ga x In 1−x As and Ga x In 1−x P. The calculations have been done by the SIESTA method 5 for cubic 64-atom supercells, with one or two cation atoms substituted by impurity species, that corresponds to impurity contents of 3% and 6%, respectively. The initial unconstrained structure relaxation for each supercell chosen was followed by a calculation of phonons by nite displacement technique. Each of the atoms in the supercell were subject to 6 consecutive small cartesian displacements, and the forces induced on all atoms in the supercell resulted in corresponding force constants. The analysis of results is the simplest for Be x Zn 1−x Se, a system with large contrast in masses and elastic properties between its parent compounds, that leads to a big separation between Zn-related and Be-related phonon modes (see Ref. 4 for details). Fig. 1 shows the phonon