Augmented spherical wave

Williams, A.R., Kiibler, K. and Gelatt, C.D. (1979). Cohesive properties of metallic compounds Augmented-spherical-wave calculations, Phys. Rev. B 19,... 

The results of our band structure calculations for GaN crystals are based on the local-density approximation (LDA) treatment of electronic exchange and correlation [17-19] and on the augmented spherical wave (ASW) formalism [20] for the solution of the effective single-particle equations. For the calculations, the atomic sphere approximation (ASA) with a correction term is adopted. For valence electrons, we employ outermost s and p orbitals for each atom. The Madelung energy, which reflects the long-range electrostatic interactions in the system, is assumed to be restricted to a sum over monopoles. 

The augmented spherical wave method (ASW) describes the valence electrons by a set of spherical waves centred round ionic cores described by atomic orbital-like functions. ... 

This monograph is based almost entirely on the work of O.K. Andersen. It is therefore appropriate to reveal the sources of the material presented, and at the same time give a brief history of the development of linear methods. At present several types of such methods are used, e.g. the linear muffin-tin orbitals (LMTO) method [1.19], the linear augmented plane-wave (LAPW) method [1.19], the augmented spherical-wave (ASW) method [1.20], and the linear rigorous cellular (LRC) method [1.15]. Of these the LMTO method, which was the earliest, will be our main concern. 

The augmented spherical-wave method of Williams et al. [1.20] appeared in 1979 and is an efficient computational scheme to calculate self-consistent electronic structures and ground-state properties of crystalline solids. According to its inventors it is a "direct descendant of the LMTO technique", and a comparison will show that the two methods are indeed very similar. 

There has been less interest in phases of the heavier homologs of the group-14 elements. There are indications that )5-NaSn, which contains tetrahedral S114 imits, is metallic and augmented spherical-wave calculations reveal a small indirect... 

Within third-generation LMTO theory, also called NMTO theory, the Taylor series is not truncated after the second term but extended to go up to Nth order, thereby increasing its accuracy [235]. The augmented spherical wave (ASW) method [236] closely resembles LMTO theory despite a few technical differences (chosen energy for linearization and exact shape of the analytical envelope function). 

Figure 8.7 The augmented plane wave and the augmented spherical wave. Both are used for representing the electron waves in the interatomic region.

The authors of [20] used the method of augmented spherical waves (ASW) for calculation of bulk moduH and cohesive energies of metals. Figure 8.7 (lower part) shows the augmented spherical waves that are applied for simulating of interatomic electron waves. 

Self-consistent ab initio band-structure calculations using the augmented-spherical-wave method have been carried out by Coehoom (1990) for hypothetical YFen and YFei2-jM t (M=Ti, V, Cr, Mo, and W). The calculated value of magnetic moment per Fe atom is 2.02 Ub, in good agreement with experiment, particularly if one takes into account that the experimental total moment also contains a small orbital contribution. 

Magnetoacoustic quantum oscillations were obtained for LaAg (Niksch et al. 1987). Two kinds of ellipsoidal Fermi surfaces, denoted by a and ji, were observed, as shown in fig. 17. The solid lines are theoretical ones based on relativistic self-consistent Augmented Spherical Wave (ASW) calculations. 

ASW augmented spherical wave k wave vector of electron... 

Linearized band structure methods were developed in the 1970s the linearized augmented plane wave (LAPW) method (36), the linear combination of muffin-tin orbitals (LMTO) method (37), the augmented spherical wave (ASW) method (38), and some others. In the LAPW method a warped muffin tin potential is frequently used, in which the real shape of the crystal potential in the interstitial region between the atomic spheres is taken into account. In the LMTO and ASW approaches the atomic sphere approximation (ASA) is frequently applied, in which— contrary to the muffin-tin approximation—overlapping atomic spheres are used. The crystal potential in the spheres is again assumed to be spherically symmetric. The sum of the atomic sphere volumes must be equal to the total volume of the unit cell. No interstitial space remains. 

As stated, the lattice parameter in ZrN shows an unusual dependence on the composition. It shows a decrease in the N-rich side and remains constant in the Zr-rich side (I). The augmented spherical wave (ASW) calculations of Schwarz et al. show the lattice parameter around 4.52 A in ZrsN4, where 25% of Zr sites are left vacant (13). The progressive decrease of the lattice parameter down to 4.556 A in the N-implanted ZrN films at HT, therefore, suggests incorporation of most of the implanted N atoms in the substitutional sites, leaving vacancies at Zr sites, whereas the increase of the lattice parameter in the samples implanted at RT could be due to... 

Eriksson and J. Wills, in The augmented spherical wave method a comprehensive treatment, edited by H. Dreysse, Lecture Notes in Physics, vol. 535, pp. 247-285 (Springer, Berlin/Heidelberg, 1999). 

---