An augmented space approach to the study of phonons in disordered alloys : comparison between the itinerant coherent-potential approximation and the augmented space recursion (original) (raw)
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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.
Interplay of force constants in the lattice dynamics of disordered alloys: An ab initio study
Physical Review B, 2014
A reliable prediction of interatomic force constants in disordered alloys is an outstanding problem. This is due to the need for a proper treatment of multisite (atleast pair) correlation within a random environment. The situation becomes even more challenging for systems with large difference in atomic size and mass. We propose a systematic density functional theory (DFT) based study to predict the ab-initio force constants in random alloys. The method is based on a marriage between special quasirandom structures (SQS) and the augmented space recursion (ASR) to calculate phonon spectra, density of states (DOS) etc. bcc TaW and fcc NiPt alloys are considered as the two distinct test cases. Ta-Ta (W-W) bond distance in the alloy is predicted to be smaller (larger) than those in pure Ta (W), which, in turn, yields stiffer (softer) force constants for Ta (W). Pt-Pt force constants in the alloy, however, are predicted to be softer compared to Ni-Ni, due to a large bond distance of the former. Our calculated force constants, phonon spectra and DOS are compared with experiments and other theoretical results, wherever available. Correct trend of present results for the two alloys pave a path for further future studies in more complex alloy systems.
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.
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.
Physical Review B, 2011
There has been increasing evidence about the effects of short-range order (or local chemical environment effects) on the lattice dynamics of alloys, which eventually affect the vibrational entropy difference among various phases of a compound, and hence their relative stability. In this article, we present an ab initio calculation of the lattice dynamics and the vibrational entropy of disordered systems with short-range order. The features in the phonon density of states were found to change systematically with chemical short-range order in the alloy. Plausible explanations for our smaller value of vibrational entropy of mixing compared to experiment are given in some detail. A general trend of the magnitude of vibrational entropy of mixing is explained by making a connection to the phonon lifetime broadening, an intrinsic property of any multiple scattering phenomenon. We illustrate the method by applying it to a body-centered cubic Fe 1−x Cr x alloy.
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.
First Principles Theory of Disordered Alloys and Alloy Phase Stability
NATO ASI Series, 1994
Carlomethods or the CVM. The difficulty with such an approacnistnatcomplex electronically mediatedinteractions aremapped ontoaneffective classical Hamiltonian. Unfortunately, thereisno apriori guarantee thatsucha procedure iseither uniqueor " rapidly convergent. In addition, since theparameters areextracted from calculations on smallunitcell systems, thereispossible thattheinteractions contain contributions (e.g. fromtheMadelnng energy) thatwill excessively favor suchstructures withrespect tothe disordered phase. Inthese lecture noteswe shall reviewtheLDA-KKR-CPA method fortreating the electronic structure and energetics ofrandom alloys and theMF-CF and GPM theories ofordering and phasestability thathavebeenbuilt on theLDA-KKR-CPA description ofthedisordered phase.Thus,we takethepoint ofviewthatmuch can be learned about metallic alloys by first studying theelectronic structure and energetics ofideal random solid solutions, which,forentropic reasons, arethenatural hightemperature solid state phasesand thento investigate their instabilities to theeither phaseseparation or to theformation ofspecific orderedphases. We shall stress thata direct connection can oftenbe made betweenspecific features intheelectronic structure associated withthe random solid solution and thedriving mechanismsbehindspecific ordering phenomena. Consequently, our understanding ofphasestability willbe underpinned by the same electronic structure thatisresponsible fordetermining theresidual resistivity and other properties ofthedisordered phaseand thatcan be experimentally verified usingoptical spectroscopies, positron annihilation and otherprobes. These lecture notesare structured as follows. In section 2 we layout the basic LDA-KKR-CPA theory oftheelectronic structure and energetics ofrandom alloys and some examplesof itsapplications to theelectronic structure and energie_ ofrandom alloys arepresented. In section 3 we reviewtheprogress thathas beenmade overthe last few yearsin understanding the mechanismsbehindspecific ordering phenomena observed inbinarysolid solutions basedon theMF-CF and GPM theories ofordering and phasestability. We will giveexamplesofa variety ofordering mechanisms:Fermi surface nesting, band filling, off diagonal randomness, charge transfer, size difference or local strain fluctuations, and magnetic effects. Ineachcasewe will trytomake thelink betweenthespecific ordering phenomenon and the underlying electronic structure of thedisordered phase.Insection 4 we will review theresults ofsome recent calculations on theelectronic structure of_-phaseNicAl1_c alloys usinga version oftheLDA-KKR-CPA codes that has been generalized to systems having complex lattices. In section 5 " we provide a few concluding remarks. 2 Theory of Random Substitutional Alloys 2.1 LDA-KKR-CPA The LDA-KKR-CPA method for calculating the energy and other properties of random solid solution alloys rests on three theoretical developments: the local density approximation to density functional theory, multiple scattering theory for solving the effective single particle SchrSdinger equation that is at the heart of the LDA-DFT self-consistent field equations, and the coherent potential approximation for treating the effects of disorder on the electronic structure i.e. for accomplishing the task of configuradonal averaging inherent in the calculation of observables. 2.1.1 Local Density Approximation and Random Alloys Density functional theory (DFT) is, in principle, an exact method for calculating the energetics of an electron system in the field of the atomic nuclei [4],[5], [21],[22],[6]. The. central result of DFT is that the total ground state energy, ELo], of a system of electrons in the presence of the external field provided by the nuclei is a unique functional ELo] = TIp] + U[p] + E,c[p] of the electron density, p(r-'),where Tip], U[p] and E,c[p] are the kinetic, potential and exchange correlation energies respectively. Furthermore, E[p] takes on its minimum value for the correct ground state p(r-').This minimum principle taken together with the constraint foo dar p(r) = N, the total number of electrons in the system leads to a set of self-consistent field equations whose solution yield the ground state charge density and hence the ground state energy. These basic equations of DFT are made into a practical computational method by making the local density approximation (LDA) in which the unknown, but exact, exchange correlation functional for the inhomogeneous interacting electron gas appropriate to the solid is approximated, at each point in space, r, by the exchange correlation functional, E_A[p], appropriate to an interacting but homogeneous electron gas having the density found at that point. Given the specification of a solid in terms of a set of atomic positions, {R/}, and corresponding nuclear charges, {Zi}, of the atoms occupying these sites, the practical applications the LDA involves the solution of a set of Hartree like, Kohn-Sham selfconsistent field equations that take the form [-V 2-I-v,s! (F;p(e; {P_}; {Zi}))] tb, Cr-') = _&,C r-') (1) J where the crystal potential ve!t(F; p(F; { R/); { Zi })) takes the form @ _2Z _ dFp(_') , [_-R'i[ + 2 IF-JI + v.=(r;'°p(r-')) (2) and where p(F; {R_}; {Zi})is given in terms of the eigen-solutions of eq. 1 as I¢,.(r-')12f(e.-p) (3)
Coarse-grained density functional theory of order-disorder phase transitions in metallic alloys
Physical Review B, 2009
The technological performances of metallic compounds are largely influenced by atomic ordering. Although there is a general consensus that successful theories of metallic systems should account for the quantum nature of the electronic glue, existing non-perturbative high-temperature treatments are based on effective classical atomic Hamiltonians. We propose a solution for the above paradox and offer a fully quantum mechanical, though approximate, theory that on equal footing deals with both electrons and ions. By taking advantage of a coarse grained formulation of the density functional theory [Bruno et al., Phys. Rev. B 77, 155108 (2008)] we develop a MonteCarlo technique, based on an ab initio Hamiltonian, that allows for the efficient evaluation of finite temperature statistical averages. Calculations of the relevant thermodynamic quantities and of the electronic structures for CuZn and Ni3V support that our theory provides an appropriate description of orderdisorder phase transitions.
Nature Communications, 2022
High-Entropy Alloys (HEAs) are a new family of crystalline random alloys with four or more elements in a simple unit cell, at the forefront of materials research for their exceptional mechanical properties. Their strong chemical disorder leads to mass and force-constant fluctuations which are expected to strongly reduce phonon lifetime, responsible for thermal transport, similarly to glasses. Still, the long range order would associate HEAs to crystals with a complex disordered unit cell. These two families of materials, however, exhibit very different phonon dynamics, still leading to similar thermal properties. The question arises on the positioning of HEAs in this context. Here we present an exhaustive experimental investigation of the lattice dynamics in a HEA, Fe 20 Co 20 Cr 20 Mn 20 Ni 20 , using inelastic neutron and X-ray scattering. We demonstrate that HEAs present unique phonon dynamics at the frontier between fully disordered and ordered materials, characterized by longpropagating acoustic phonons in the whole Brillouin zone. Recently, a new family of crystalline metallic materials has been discovered and has come to the forefront of materials research for their exceptional mechanical properties: High-Entropy Alloys (HEAs) 1-4. Obtained with casting techniques from the melt, HEAs are singlephase, equiatomic alloys with four or more elements that are evenly dispersed in an average ordered, close-packed, and simple crystalline structure, forming a random solid solution 5,6. The strong chemical disorder within the unit cell introduces disorder at a larger lengthscale, as the periodically repeated unit cell is in fact always different due to the random atomic arrangement within it. As such, the translational invariance is disrupted, drawing these materials closer to glasses. Indeed, HEAs share with these latter the presence of a distribution in atomic sizes, masses and force-constants, usually absent or present only in a limited extent in crystalline materials. Moreover, HEAs also exhibit thermal transport properties quite similar to glasses: thermal conductivities that are much lower than in simple metals, going from some tens of W/mK 7 down to less than 2 W/mK 8 , and a low and almost temperature independent lattice contribution 9,10. In glasses, the emergence of a low and weakly temperature dependent lattice thermal conductivity has been ascribed to a strong phonon scattering due to the intrinsic disorder, which includes topological, mass and forceconstant disorder 11-13. While there are indications that force-constant disorder at the nanoscale is mainly responsible for such strong scattering 13-15 , it is experimentally impossible to separate the effect of
Lattice dynamics of metals from density-functional perturbation theory
Physical Review B, 1995
The density-functional perturbation theory approach to lattice-dynamical calculations is extended to metallic systems. The smearing technique is used to deal with the Fermi surface and its variational formulation is restated. First-principles phonon dispersions of Al, Pb and of the transition metal Nb are in good agreement with available experimental data. In particular an accurate description of the anomalies observed in lead and niobium is obtained.