General perturbation method

In table 1 we present the results for the EPIs up to the fourth nearest neighbors obtained from the KKR-CPA coupled with the generalized perturbation method(GPM) along with our calculation for 50-50 PdV alloy. ... 

We define a fee lattice and affect at each site n, a spin or an occupation variable <7 which takes the value +1 or —1 depending on whether site n is occupied by a A or B atom. Within the generalized perturbation method , it has been shown that substitutional binary alloys AcBi-c may be described within a Ising model with effective pair interactions with concentration dependence. Thus, the energy of a configuration c = (<7i,<72,- ) among the 2 accessible configurations for one system can be written... 

Ab-initio studies of surface segregation in alloys are based on the Ising-type Hamiltonian, whose parameters are the effective cluster interactions (ECI). The ECIs for alloy surfaces can be determined by various methods, e.g., by the Connolly-Williams inversion scheme , or by the generalized perturbation method (GPM) . The GPM relies on the force theorem , according to which only the band term is mapped onto the Ising Hamiltonian in the bulk case. The case of macroscopically inhomogeneous systems, like disordered surfaces is more complex. The ECIs can be determined on two levels of sophistication ... 

Introduction of partial order at finite temperatures adds another level of complexity and difficulty. This situation is handled by the cluster variation method (CVM) free energy functional, which is expressed as a function of multisite correlation functions, whose coefficients are obtained by the generalized perturbation method (GPM) or the embedded cluster method (ECM). All of these methods are highly computationally intensive at present, this area is probably the principal frontier of alloy phase theory. 

Furthermore, a chapter which discusses different ways to perform calculations for disordered systems is presented, including a description of the Coherent Potential Approximation and the Screened Generalized Perturbation Method. A comparison between the Exact Muffin-Tin Orbital method and the Projector Augmented-Wave method in the case of systems exhibiting both compositional and magnetic disordered is included as well as a case study of the MoRu alloy, where the theoretical and experimental discrepancies are discussed. 

There are a number of other methods which may be used to obtain approximate wave functions and energy levels. Five of these, a generalized perturbation method, the Wentzel-Kramers-Brillouin method, the method of numerical integration, the method of difference equations, and an approximate second-order perturbation treatment, are discussed in the following sections. Another method which has been of some importance is based on the polynomial method used in Section 11a to solve the harmonic oscillator equation. Only under special circumstances does the substitution of a series for 4 lead to a two-term recursion formula for the coefficients, but a technique has been developed which permits the computation of approximate energy levels for low-lying states even when a three-term recursion formula is obtained. We shall discuss this method briefly in Section 42c. 

S. Bocriu and G. P. Ceechini, "Sensitivity Coefficients Calculation Using Direct and Generalized Perturbation Methods," RT/FI(73)14, Comitato Nazionale per I Etiergia Nuclearc (1973). 

H. Mitani and K. Hideo, Sensitivity Coefficients of Integral Data and Generalized Perturbation Method, JAERl-M-4760 Jap. At. Energy Res. Inst. (1972). 

Drchal, V., Pasturel, A., Monnier, R., Kudrnovsky, J., and Weinberger, P. (1999) Theory of surface segregation in metallic alloys the generalized perturbation method. Comput. Mater. Sci., 15, 144. 

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