Calculations of Densities of States for Nonrandom, Substitutionally Disordered Alloys
- PDF / 1,199,514 Bytes
- 8 Pages / 415.8 x 637.2 pts Page_size
- 59 Downloads / 197 Views
CALCULATIONS OF DENSITIES OF STATES FOR NONRANDOM, DISORDERED ALLOYS
A. Gonis and A.J.
SUBSTITUTIONALLY
Freeman
Department of Physics and Astronomy and Materials Research Center, Northwestern University, Evanston, IL 60201 USA
INTRODUCTION Disordered systems have received a great deal of theoretical attention in the last fifteen years or so, and many advances in our understanding of such systems have been made. The greatest progress has been made in connection with substitutionally disordered alloys in which atoms of various species are randomly distributed over the sites of a regular lattice. The most satisfactory single-site theory for studying the properties of random substitutionally disordered alloys, in particular the one-particle properties such as the density of states (DOS), is the coherent potential approximation (CPA) [1,2]. In the CPA, one considers that the real disordered material is replaced by a self-consistently determined effective medium which is characterized by an energy-dependent site-diagonal selfenergy, and which preserves all symmetries of the lattice. The CPA yields unique and analytic results, i.e., yields DOS and spectral weight functions that are nonnegative and satisfy the fundamental sum rules. There exist several reviews of the CPA [3-5] both for systems describable by tight binding (TB) and by muffin-tin (MT) Hamiltonians. In spite of its many desirable properties, however, the CPA, as a single-site theory, suffers from various limitations. The most important among these is the inability of the CPA to account for many-site statistical fluctuations. Also, the CPA is applicable only to random alloys and cannot treat effects such as short range order (SRO), which are known to be present in many disordered systems. In order to remove these limitations, several multisite extensions of the CPA have been proposed [6-19]. Although initially promising, many of these theories were found to be too difficult to implement computationally and to violate the symmetry of the underlying lattice, such as the molecular CPA [17], to suffer from analytic difficulties [18], or to involve severe approximations, such as the replacement of the real lattice of the material by Cayley tree (Bethe) lattice [19]. A cluster method which strikes a balance between conceptual simplicity and computational ease, and which always yields meaningful physical results and takes full account of the symmetry of the lattice is the embedded cluster method (ECM) [20,21]. In this method, one treats a compact cluster of atoms embedded in an effective medium which is determined in some optimal way, such as in the CPA. Introduced [20] in connection with TB systems, the ECM has recently been extended to alloys describable by MT Hamiltonians [22,23]. The embedded cluster method can be used to calculate many physical properties substantially more accurately than it is possible in the CPA. Thus, one can calculate the DOS of substitutionally disordered alloys with known degrees of SRO. In addition, one can make quantitative stateme
Data Loading...
