Density of states from moments. Application to the impurity band

Gaspard, Jean-Pierre; Cyrot‐Lackmann, F.

doi:10.1088/0022-3719/6/21/012

Cited by 240 publications

(81 citation statements)

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“…22 That is, from the second to the fifth moments we compute the coefficients b 1 , a 1 , b 2 , and a 2 of the recursion method. Since the coefficients a n , b n are convergent oscillating series, 23 their limit a ϱ , b ϱ is estimated as a ϱ ϭ(a 1 ϩa 2 )/2 and b ϱ ϭ(b 1 ϩb 2 )/ 2, and the coefficients a n , b n with nϾ2 are assumed to be equal to a ϱ , b ϱ which gives rise to the well-known square root terminator of the continued fraction expansion of the diagonal elements of the Green function. 24 The integration of the LDOS in order to obtain the bond energy is performed numerically.…”

Section: ͑23͒mentioning

confidence: 99%

Development of a tight-binding potential for bcc Zr: Application to the study of vibrational properties

Porta

Castán

2001

Phys. Rev. B

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We present a tight-binding potential based on the moment expansion of the density of states, which includes up to the fifth moment. The potential is fitted to bcc and hcp Zr and it is applied to the computation of vibrational properties of bcc Zr. In particular, we compute the isothermal elastic constants in the temperature range 1200 KϽTϽ2000 K by means of standard Monte Carlo simulation techniques. The agreement with experimental results is satisfactory, especially in the case of the stability of the lattice with respect to the shear associated with CЈ. However, the temperature decrease of the Cauchy pressure is not reproduced. The Tϭ0 K phonon frequencies of bcc Zr are also computed. The potential predicts several instabilities of the bcc structure, and a crossing of the longitudinal and transverse modes in the ͑001͒ direction. This is in agreement with recent ab initio calculations in Sc, Ti, Hf, and La.

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Section: ͑23͒mentioning

confidence: 99%

Development of a tight-binding potential for bcc Zr: Application to the study of vibrational properties

Porta

Castán

2001

Phys. Rev. B

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“…Or one can aim for exact results on the bounds of the integrated density of states, and then determine the best density of states. A detailed comparison of these various methods [4] shows that the more powerful method is based on expansion of the Hilbert transform G(z) of the density of states into a continued fraction [6] The coefficient a, is a function of the k first moments, po, pl, ..., pk- [4,5,71. These coefficients a, are very rapidly converging towards their asymptotic value and the way they converge can be simply related to the properties of the density of states (possible singularities and band gaps).…”

Section: F Cyrot-lackmannmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The behaviour of the density of states near its edges can be shown to be related to the asymptotic behaviour of b, [4]. In particular, when the band shows internal singularities, the coefficients b,, are decreasing in oscillating with a frequency connected to the position of the singularity and a damping function related to the nature of the singularity.…”

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confidence: 96%

“…So, one has to use a technique to estimate the density of states from its low-order moments. Several methods have been used, but the one which seems the most precise and powerful as shown by a detailed comparison [4], is based on a continued fraction expansion of the Hilbert transform of the density of states.In a first part, we describe the general features of the moment expansion technique. Then, we describe the continued fraction method for deriving the density of states from the low-order moments.…”

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Expansion in Moments and Disordered Systems

Cyrot‐Lackmann

1974

J. Phys. Colloques

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RBsumB. -On montre que la technique de developpement en moments de la densitt d'ttats est un outil tres utile pour l'etude des systemes desordonnes. Les moments peuvent &re calculCs directement comme une fonction des integrales de recouvrement et de l'ordre local caractkrisant le systeme. Parmi les techniques possibles pour obtenir la densite d'ttats a partir de la seule connaissance de ses premiers moments, la meilleure repose sur un developpement en fraction continue de sa transforrnee de Hilbert. Cette methode est brikvement discutee, et I'on montre comment des informations prbcises peuvent 6tre obtenues sur d'6ventuelles bandes d'energie interdite ou d'eventuels points critiques dans la densite d'etats.On donne ensuite des exemples des applications possibles de la methode des moments k different~ cas de systemes dbordonnb. Dans le cas des systemes a dksordre de composition, c'est-Adire par exemple des alliages dtsordonn6s, cette methode permet une nouvelle simple dkviation de I'approximation de potentiel cohkrent, et peut &tre utiliske pour obtenir des resultats etendant cette approximation.Dans le cas des systemes avec desordre topologique, c'est-a-dire par exemple les metaux liquides ou les bandes d'impuretes, on donne des densites d'etats detaillees, en utilisant en particulier une approche de simulation de ces systkmes sur ordinateur.Abstract. -Expansion of the density of states in its moments is shown to provide a useful tool in the study of the electronic properties of tightly bound disordered systems. The moments can be directly computed as a function of the overlap integrals and the local order of the system. Among the possible techniques for obtaining the density of states from its low order moments, the best one, using a continued fraction expansion of its Hilbert transform, is briefly discussed. It is also shown how information about the possible band gaps and the remnants of critical points structure can be obtained through this technique. Examples of the possible applications of the moment method to various cases of disordered systems are then given. For systems with compositional disorder, i.e. disordered alloys, this approximation which provides a new simple derivation of the coherent potential approximation (CPA), can be used to obtain results extending the CPA. For systems with topological disorder, i.e. impurity bands of liquid metals, detailed density of states are given, using in particular a simulation of the random system on the computer. Introduction.-This paper concerns a method recently developed to study the electronic properties of tightly bound disordered systems. Much research has been performed in this domain, where great difficulties arise due to the breakdown of the usual approach based on the periodicity of the lattice. Most of the results obtained are derived for one-dimensional disordered systems [I], but unfortunately neither the methods nor the results can in general be extended to the three-dimensional case.The method presented here, based on an expansion of the electron...

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Basic Properties of Well‐Known Intermetallics and Some New Complex Magnetic Intermetallics

Entel

2017

Handbook of Solid State Chemistry

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The structural, electronic, and magnetic properties of novel functional magnetic intermetallics, in particular some of the most prominent magnetic Heusler alloys, have been reviewed with emphasis on their complex magnetic behavior and nonergodic glassy features, in contrast to the well‐known properties ofTi‐NiandNi‐Alshape memory alloys. Calculational procedures have been listed throughout the text and the theoretical results have been compared with experimental findings where possible. The thermodynamic properties of a few systems (Ni–Co–Mn–In), which undergo a structural phase transformation of displacive nature in conjunction with a metamagnetic first‐order phase transition, have been discussed in detail. The importance of such magnetostructural phase transition together with the so‐called thermodynamic (kinetic) arrest phenomenon for the appearance of a giant magnetocaloric effect has been underlined. The list of references should allow bridging the gap between shape memory alloys such asTi–Ni(including recentab initiocalculations that explain the rapid decrease of the martensitic transformation temperature with disorder) and the “exotic properties” of the magnetic intermetallics.

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Density of states from moments. Application to the impurity band

Cited by 240 publications

References 19 publications

Development of a tight-binding potential for bcc Zr: Application to the study of vibrational properties

Development of a tight-binding potential for bcc Zr: Application to the study of vibrational properties

Expansion in Moments and Disordered Systems

Basic Properties of Well‐Known Intermetallics and Some New Complex Magnetic Intermetallics

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